Statistics Flashcards
(179 cards)
1
Q
What Latin word is statistics derived from?
A
Status.
2
Q
What’s the purpose of statistics?
A
To help us get information out of large amounts of numbers and data.
3
Q
What 2 main branches does statistics fall under? And which is this module about?
A
- Descriptive statistics; which focuses on collecting, summarising, and presenting a set of data.
- Inferential statistics; analyses sample data to draw concultions from a population to make decisions.
This module focuses on descriptive statistics.
4
Q
Why does statistics actually exist?
A
Because psychologists, engineers, medical researchers and economists built it, and they build it because they needed it.
5
Q
Another term for whole numbers and what do they consist of?
A
Integers. 0-9
6
Q
What’s the numerator and what’s another term for it?
A
It’s also called the dividend. The one on top.
7
Q
What’s the denominator and what’s another term for it?
A
The one at the bottom. Divisor.
8
Q
What’s another term for dividing?
A
Quotient
9
Q
What’s a proper and improper fraction?
A
A proper fraction is one which the numerator is less than the denominator.
10
Q
How do you add fractions?
A
1/5 + 2/5 = 1+2/5
11
Q
What is HCF? And where is it used? And how’s it work?
A
Highest common factor. Used to multiply fractions.
12
Q
How do you divide fractions?
A
13
Q
What 3 components do decimals consist of?
A
An integer, followed by a decimal point, followed by another integer.
14
Q
How do you add decimals?
A
15
Q
How do you times decimals?
A
16
Q
How do you divide decimals?
A
17
Q
What does percent mean?
A
Per hundred.
18
Q
How do you calculate a percentage rate of an amount?
A
R = P/B
Portion/Base
19
Q
What is an exponent?
A
A number that is written as a superscript to another number called the base.
20
Q
How do you times and divide exponents?
A
21
Q
Solve x
A
22
Q
What does 4 ^ 0 = to?
A
1.
23
Q
What’s 0 ^ 0?
A
Undefined.
24
Q
Define statistics.
A
Statistics is the scientific method that enables us to collect, organize, analyse, and interpret data in order to make decisions as responsibly as possible.
25
What's the 2 main characteristics of Statistics?
* **Data;** numerical facts
* **Information;** knowledge communicated
26
Describe the decision-making process.
1. Collect relevant information as reliable as possible.
2. Select parts most helpful.
3. Make the decisions as sensibly as possible.
4. Perceive the risks in the decision and evaluate the corresponding risks of alternative decisions.
27
What's statistics used for in economics and commerce?
* To assist in designing statistical methodology for best effect.
* To draw inferences and predict the future.
28
What is data?
Data is a scientific term for a collection of facts such as values or measurements for a specific topic of interest.
29
What's are data sets?
Are collections of organized data that can be used for analysis such as, population, and sample.
30
What is population in statistics?
The totality of the population of all objects that are interested in studying at any one moment.
31
What's a parameter?
It's a numerical value that summarises a characteristic of the entire population.
32
Define sample.
A subset of the population which will be expected to be a good representation of the population.
33
Define a statistic.
It's a numerical value used to describe or summarise the characteristics of a sample.
34
What is a variable?
A variable is a phenomenon which changes with respect to the influence of other phenomena or objects.
35
What 2 types of variables do you get and briefly explain them.
* Dependent variables; their magnitude depends on the magnitude or the presence of other variables.
* Independent variables; are those phenomena which are capable of influencing other variables without being themselves influenced.
36
What is a model?
A theoretical construction of all expected interrelationships of facts and figures which cause and affect any natural physical or social phenomenon.
37
What do models attempt?
They attempt to construct a simplified explanation of the complex reality in a manner which can be easily understood, and whose nature can generally be said to be possible at all times.
Consumers can only be modelled because we can't lock them up.
38
What is an index?
It's an imprecise and imperfect measure of some underlying concept variable which is not directly measurable, which is only capable of indicating a trend.
39
What acronym is there for the basic operations of algebra?
BODMAS
Brackets, Orders, Division, Multiplication, Addition, and finally Subtraction.
40
What types of variables do you get? And what are the off sets of them?
* Qualitative variables; descriptive information that can be devided into categories. (Colour, gender, type of vehicle).
* Quantitative variables; are measured numerically which can be split into 2:
1. Discrete variables; whole
numbers. (No. of students in a class).
2. Continuous variables. (A person's height & time in a race).
41
What are the 2 main groups of data?
* Primary data; collected especially for this soecific survey that is being conducted.
* Secondary data; data already collected from elsewhere, for some other purpose, but which can be used.
42
What ways can statistical data be obtained?
Measurements and counts.
43
What categories can data be classified into? Explain.
* **Nominal data;** lowest level of measurement. Classify data qualitatively by name. (Cats as black and white). Impossible to arrange and rate them.
* **Ordinal data;** differentiation with size, has magnitude and direction. Can be arranged in order but not rated. (Low income, Middle Income, High income).
* **Interval data;** has magnitude and direction. It has equal intervals but the weakness of this data is that the position of 0 is unclear. (Temperature). It can be rated but ratios are difficult to compute.
* **Ratio data;** the highest level of measurement, with transitivity; magnitude and direction; equal interval qualities; and the zero can be identified. Ratios are possible. (Height, weight, profit, age).
44
Why do we sample data?
* Unpractical to analyse all data.
* Not physically possible.
* Too expensive
* Situation, sampling needs to be done quickly.
45
What are some things to keep in mind in order to collect data most efficiently?
1. Sample it from the population.
2. Sample must be unbaised otherwise ti will be worthless.
3. Implement sample rules to help eliminate bias in sampling.
4. Sampling errors are inevitable. Asses how much variation can be expected to occur.
5. Sample randomly
46
What are some rules that will help prevent biased sampling?
* Do not only use people that volunteer.
* Do not choose a sample using a method that omits segments of the population.
* Do not use people in the sample only because they are available.
* The person selecting the sample should not have a vested interest in the results.
47
What are some questions to ask before sampling data?
* What should the size of the sample be?
* What precisely are the **members** from which the sample is to be chosen.
* How should the members be selected for inclusion?
Sample size will depend on the type of problem and the desired accuracy?
48
What are some ways conduct random sampling correctly?
*Random numbers can be generated by a software program or a calculator.
*Population members are assigned a number.
*Sample is then chosen to randomly chosen numbers.
49
What are other methods of sampling other than random sampling and explain them.
* Systematic sampling: by selecting every nth time after a random start. Sampling intervals.
* Quota sampling: population is divided into **subgroups** based on characteristics. Then researchers select representatives from the quotas **non-randomly**.
* Stratified sampling: dividing the population into strata or **categories**. **Random** samples are then taken from each stratum or category.
* Cluster sampling: a **non-random** sampling method that involves dividing the population into **pre-existing groups** and then **randomly** selecting entire clusters as a sample.
* Multistage sampling: a probability sampling method which involves dividing the population into a number of sub-populations and then selecting a small sample of these sub-populations at random. Each sub-population is then divided further, and then a small sample is again selected at random.
50
How should a survey or questions be designed to maximize efficiency?
*Questions should be designed that allow the person the freedom to give his or her honest opinion.
*Questions should be open ended, multiple choice and open for interpretation.
*The person completing the questionnaire should do so confidentiality, as their opinions should not be made known to others.
51
The type of visual representation you choose depends on what?
It depends on the type of variables you are dealing with within your data set. Nominal, ordinal, Interval, ratio data.
52
What are some data preparation rules?
Data presented must always be:
* Factual
*And relevant
Before presentation always check the source of the data to ensure that the:
*Data has been accurately transcribed
*Figures are relevant to the problem
53
What are some important points that should be followed when constructing a table?
* A clear label for the table.
* The type of information in the actual table should be properly titled.
* Rows and columns should be precise, and units of the values included.
* Clearly state the units.
* Show percentages and ratio where appropriate.
* Categories should not overlap.
* Correctness of calculations should be verified.
* Omit any unnecessary or irrelevant data.
* Use your imagination and common sense.
54
Why are tables better than narratives for data?
Because they are much more compact and helps us distiguish patterns.
55
In what way are graphs better in representing data than tables?
They better depict relationships between variables and more than one set of data can be displayed on a graph.
56
What are some points to keep in mind when constructing a graph?
* Give an appropriate title.
* Label the axes x & y with units of measurement.
* Do not plot too many curves on the same set of axes.
* Accompany the graph with the table of data.
* Show the 0 on each scale.
57
What is a pie chart use for?
To give a visual presentation of data to indicate the proportions that make up a given total.
58
What is a pie chart?
A circle that is divided into sectors by lines, in such a way that the area of each sector is proportional to the size of the quantity represented by that sector.
59
What is a bar chart?
A series of rectangular bars where the length of each bar represents the actual magnitude of the respective quantities.
60
What are some guidelines for preparing a bar chart?
* Make widths of each bar equal.
* Clearly label the axes
* Include footnotes, source data and tables
61
What's the purpose of creating a multiple bar chart?
To emphasize comparison.
62
What is a pictogram?
A graph in which data is displayed using pictures.
63
What's a scatter diagram used for?
To display the relationship between 2 quantitative variables. It displays data points as dots on a 2 dimensional graph. For example, the relationship between advertising and sales.
64
Which axes does the dependant and independent variables go on?
Independent (the cause) - x-axis
Dependent (the effect) - y-axis
65
What is a positive relationship between to variables refer to?
This means their values tend to increase together and decrease together.
66
What's the difference between a non-linear & linear relationship?
67
What is a negative linear relationship?
When 2 variables move in opposition directions and the scatter diagram consists of points that appear to cluster around a straight line.
68
What is raw data and what's wrong with it?
Raw data is unprocessed data and is difficult to distinguish any pattern in the data due to to many variables.
69
What's the purpose and advantages of a frequency table?
* It solves the problem that raw data brings by summarising data in tables that report how often certain sextions appear. This helps us identify patterns and make it more understandable.
* It also helps us locate figures more quickly.
* Makes it easier to compare different classes.
70
What elements do Frequency tables have?
* **Classes or class intervals;** represent the possible data values that the variables assume AKA categories (k)
* **Class midpoint;** represents the middle value of a class interval.
* **Frequencies;** represent the number of times that observation fall within a specified class.
* **Percentage frequencies;** of the total sample size.
71
What are some rules to follow when constructing a frequency table?
* The class intervals must never overlap.
* Intervals should be if the same width.
* The first or/and last class interval could be open ended but avoided as much as possible.
* If no observations in a particular interval, it should still be included to avoid misleading impression of the data.
* Sum of frequencies equals total number of observations.
72
Why is the size of the class important?
The right size classes assists with easy reading. To many classes and information are not much better than raw data. To few classes reduces the amount of meaningful information.
73
What are some steps for constructing a frequency table from a set of raw continuous data?
1. Determine the sample size, **n**.
2. Determine the range. The difference between the largest observed value in the data set (Xmax) and the lowest observed value in the data set (Xmin). Work with round numbers.
3. Determine the number of classes, **k** by using Sturges' rule. Rule of thumb is 5-12 classes.
4. Determine the width of each class.
CW. Easier to deal with when they are in multiples of 2, 5, 10.
5. Next we determine the class limit for each class by using the CW. Eahx subsequent class is then created by adding the class width to the upper boundary of the previous class.
6. The class midpoints for each class interval.
7. Determine the frequencies for each class by tallying the observations.
74
What's different about a cumulative frequency table?
The class intervals do not have bounds.
[50; 70) **[** is including. **)** is exclusive.
75
What is a histogram?
It's a bar chart but without gaps. The height of the bar is proportional to the frequency in that particular class.
76
What's a frequency polygon?
A line graph that emphasises the continuous change in frequency. It is formed by the histogram by joining the midpoints of the top of the bars with the straight lines.
77
What's an Ogive?
Or a Cumulative frequency Polygon, is a line graph that displays the cumulative frequency at its upper boundary.
78
How do you construct a cumulative Frequency Polygon?
1. Construct a frequency distribution table that includes cumulative frequencies as one of the columns.
2. Specify the horizontal & vertical axis.
* Horizontal scale; upper class boundaries.
* Vertical scale; cumulative frequencies.
* X-axis represents the actual Lower limit of the first class.
3. Plot points that represents the upper class boundaries.
4. Connect the points in order from left to right.
5. Should start at lower boundary; end at upper boundary.
79
What's the difference between central tendency and the dispersion?
* **Central tendency:** is the statistical measure that summarizes a set of data with a single value that represents the centre of the data's distribution.
* **Dispersion:** refers to the degree in which a dataset spread out from the central tendency.
80
What's the most frequently encountered method of condensing data?
Calculating a single number is one of the most frequently encountered.
81
What are the most common measures of central tendency?
Mean, median, and mode.
82
What is the arithmetic mean?
The arithmetic mean is the sum of all observations divided by the number of observations which gives you an average. (The normal mean).
83
What's the symbol for population mean.
84
What's the symbol for a sample mean?
85
What's the symbol "N" stand for?
The population size or total amount of observations.
86
What's the formula for calculating the sample mean?
87
What does the symbol "K" represent?
Groups, categories, or classes.
88
What's a true statement about the mean drawn from a grouped frequency distribution?
Is it not possible to calculate the exact mean of the original data in a grouped frequency distribution, since the information is lost when the data is grouped.
89
What assumption do we make in the formula of a grouped frequency distribution when calculating mean?
We assume that the observations are already evenly throughout each class interval. Calculations are based on the assumption that all observations occur at the midpoint (m) of their class.
90
What's the formula for calculating the mean in a grouped frequency distribution?
91
What's the geometric mean?
The geometric mean is used in economic data to average ratios or rates of change. The arithmetic mean would be misleading for calculating the rate of change.
92
What's the formula for calculating the geometric mean?
93
What are some properties of the mean?
* The mean can only be used for quantitative data.
* The mean makes use of all observations. Of the 3, it's the only one that makes use of all observations.
* Each variable in a data set will have only 1 mean value.
94
What are outliers? And explain their impact.
Values that have been erroneously recorded are simply unusually large or small. They have the tendency to skew the data distribution when calculating the mean.
95
What is the mode?
The number that occures the most frequently in a set of numbers.
96
What happens when their are 2 numbers that have the same frequency when calculating the mode? And what's it called?
This is called bimodal. This would mean both are the mode.
97
What is the modal class?
The class frequency with the largest frequency.
98
What's the formula for calculating the mode in a grouped frequency distribution? And what do those elements all represent?
99
What is median?
It's described as the 'middle' observation in a data set that's arranged in order.
100
What's the symbol for the median?
101
What's the formula for calculating the median?
102
What's the formula for calculating the median in a grouped frequency distribution?
103
What different quartiles do you get for raw data? And what do they represent?
1. First quartile - Q1
There are 25% of the observations below Q1 and 75% above Q1.
2. Second quartile - Q2
There are 50% of observations below Q2 and 50% above Q2. Q2 is obviously the mean.
3. Third quartile - Q3
75% of observations below Q3 and 25% above Q3. Q3 is often called the upper quartile.
104
What are the formulas for calculating the 3 Quartiles for organising raw data?
105
What if the positions for Q1, Q2, Q3 are not whole numbers?
Then we use interpolation to find the values.
106
What's the formula for calculating an exact percentile?
107
What formula do you use when calculating a percentile when it's not a whole number?
108
What's the formula for the percentile in grouped frequency distribution data?
109
What is the skewness or shape of distribution measured by?
It's measured by comparing the relative positions if the mean, median, and mode.
110
What are the 3 most common shapes of distribution? And explain each.
* Symmetric shape; the distribution is identical in both sides of its central point where each left and right sides mirror eachother. Mean=median=mode.
* A uniform or rectangular distribution; is a symmetric distribution with equal or approximately equal frequencies for each class.
* A skewed-to-the-right distribution positively skewed); has a longer tail on the right side. Mode
111
What are the 3 most common shapes of distribution? And explain each.
* Symmetric shape; the distribution is identical in both sides of its central point. Mean=median=mode.
* A uniform or rectangular distribution; is a symmetric distribution with equal or approximately equal frequencies for each class.
* A skewed-to-the-right distribution positively skewed); has a longer tail on the right side. Mode
112
What is dispersion?
The degree to which numeric random variables are scattered about from their central point of distribution.
113
How do we best represent the following levels of measurement: nominal data, ordinal data, Interval/Ratio data?
114
What's a good alternative for distribution tables when underlying distribution may not be normal?
Interquartile range is a good alternative.
115
What are the measures that are used to measure dispersion?
* Range
* Interquartile range
* Variance
* Standard deviation
* Quartile deviation
116
What's the simplest measure of dispersion and explain it.
The simplest measure of dispersion is the range, which is defined as simply the difference between the largest and smallest values in a set of data.
117
What is standard deviation?
It's basically the method of finding the average spread of each observation away from the mean or the set of observations
118
What's the symbol for standard deviation? And what's the formula for calculating it?
119
What's the formula for standard deviation of a sample?
120
How do you calculate the standard deviation for frequency distribution?
121
How do you calculate standard deviation for a sample from a grouped frequency distribution?
122
What does the symbol 'K' represent in formulas for grouped frequency distributions?
The number of class intervals. Used instead of 'N' the total amount of observations.
123
What is the Empirical rule? And when can it be used?
The Empirical rule states:
* About 68% of the data lie within one standard deviation.
* About 95% of the data lie within 2 standard deviations of the mean.
* About 99.7% if the data lie within 3 standard deviations of the mean.
The Empirical rule can only be used when the histogram is symmetrical.
124
What can standard deviation be used for?
It can be used to compare the variability of several distributions and make a statement about the general shape of the distribution.
125
126
What is the standard score?
The standard score (z-score) represents the number of standard deviations a given value (x) falls from the mean.
127
What's the formula for the standard score? And whats it's symbol?
128
What is the coefficient of variation used for?
It is used to measure the changes that have taken place in a population over time, or to compare the variability of two populations that are expressed in different units of measurement. It is expressed as a percentage.
129
What's the formula for coefficient variation?
130
What is the idea of priori probability?
The quantification of the probability of an event happening through the circumstances of the given facts, before any actual data is collected.
131
What 2 things do we need to understand about probability when using it?
1. Expressed as a fraction of 1.0 that a favorable event will occur.
2. The concept of probability is a limiting factor. Ratio of favourable outcomes to the total number of trials, as this number of trials approaches infinity.
132
How is probability expressed in a formula?
P(A) = r/n
r= number of favourable outcomes
n= number of trials
A= is the favourable event.
133
What probability ratio is most likely and least likely?
Most likely is above 0.5
Least likely is below 0.5
All out of 1.0
134
What is a mutually exclusive event?
Any 2 events that cannot occured simultaneously during the same trial or in the same experiment.
Example, a head and a tail if a coin.
135
What are collectively exhaustive events?
Simply cover all possible events in a situation.
Example, (1, 2, 3, 4, 5, 6) for a dice.
136
What is an independent event?
When any 2 events with the chances of one event occuring are not influenced by the happening of the other event.
Example, the outcome of the first coin toss does not effect the outcome of the second toss.
137
What is conditional probability?
Is defined as the probability that any event will occur, given that another event has occurred.
138
What is the formula for conditional probability?
139
It indicates "on condition that".
140
Discuss the rules of probability.
1. **The multiplication rule.** If A and B are independent events, the probability of joint occurrence of these 2 events is equal to the product of the probability of the occurrence of each one of them. **As long as they are independent.**
P(H1 and H2) = P(H1) x P(H2) = 0.5 x 0.5 = 0.25
This reduces the size of the fraction due to the difficulty in having emsjch a lucky coincidence occuring in real life.
2. **Addition rule.** When one is faced with alternative events, each one of which is a success, the chances if success increase because the investigator is satisfied by any of the successes.
P(A or B) = P(A) + P(B)
**Area of overlap between 2 needs to be minused from eachother.**
Example, 4 A's and 4 Hearts in a deck. There's 1 card that over laps (queen of hearts) that needs to be minused from the probability.
141
What better counting technique can one use for probability?
The reverse way of looking at probability. Instead of asking what probability there is that an isolated may occur, one is interested in the number of alternative ways a set of events may turn out. Then the probability of one of those ways turns out is 1/n.
142
What are some counting techniques for calculating all the alternative ways an event can unfold?
* The decision tree. Involves drawing the various interconnections between them all. This is only practical for evaluating small alternatives.
* Permutations; order of arrangements are important.
* Combinations; we use when the order of arrangements of objects is not necessary.
143
What is the formula for permutation?
144
What is the formula for permutation?
145
What's the formula for combinations?
146
What are the 2 techniques for measuring the strength of possible business relationships between business management related variables?
* Regression analysis
* Correlation analysis
147
What is simple linear regression analysis?
It finds a straight line relationship between two numerically scaled random variables. One is called the dependant, and the other is call the independent variable.
148
What's the difference between the independent and dependent variable in a simple linear regression analysis?
* Independent variable **x** . It's values are normally easily determined. In certain instances, the independent variables values can be controlled.
* Independent variable **y** . It is influenced by the independent variable **x** .
x; y
Advertising levels; company turnover
Speed; fuel consumption
Daily temperature; electricity demand
149
What's the difference between regression analysis and correlation analysis?
* Regression analysis is concerned with mathematically quantifying the structural relationship between independent and dependent variables. And using that to predict eachother.
* Correlation analysis identifies the strength and direction of this association.
150
What's the formula for regression analysis?
151
What's the purpose of constructing a regression equation?
It's to estimate values of y from values of x. Estimates of y are found by substituting a given x value into the regression equation.
152
What's the purpose of correlation analysis?
It's to measure the strength of the relationship between 2 variables.
153
What 2 types of correlation coefficients do you get?
* Pearson's correlation coefficient
* Spearman's rank correlation coefficient
Their interpretation is the same.
154
What does a low correlation mean and a correlation mean?
* A low correlation does not necessarily imply that the variables are unrelated, buy simply that the relationship is poorly described by a straight line.
* A correlation does not necessarily imply a cause and effect relationship, merely an observed association.
155
What's a perfect positive correlation look like?
156
What does a negative correlation look like?
157
What does a positive direct relationship look like?
158
What does a positive direct relationship look like?
159
What does a negative indirect linear correlation look like?
160
What does a positive direct linear correlation look like with r->0?
161
What does pearson's correlation coefficient compute?
It computes the correlation between 2 numerically scaled random variables only.
162
What is Pearson's correlation formula?
163
What is an index number?
It's a measure of the change in the level of activity of a single item or collection (basket) of related items from one time period to another.
164
What's the formula for an index number? And give some examples.
165
What's the 2 major categories for index numbers?
Price & quantity.
166
What's a price index?
A price index measures the percentage change in price between 2 periods of time.
167
What's the formula for price index?
168
What is a quantity index?
It measures the percentage change in consumption level of either an individual item or a basket of items from one time period to another.
169
What's the formula for the quantity index?
170
What are weighted index numbers? And what 2 types do you get?
Weighted index numbers weighed according to their relative importance. Unlike index numbers which grant equal importance to all items.
* The fixed weight index.
* The simple weighted index.
171
What are fixed weighted index numbers? And what's formula?
A type of index number that uses a fixed set of weights from a specific base period to calculate changes in a variable over time. They don't need to be necessarily be drawn from the same period and these weights remain constant regardless of changes.
172
What's a simple weighted index? And what's its formula?
This places the base heat for both price and quantity in the numerator. Which runs the risk of a lack of representivity in the base period.
173
What's a composite index? And what 2 types do you get?
It combines the relative prices and quantities to provide an overall representation
* Laspeyres index
* Paasche index
174
What is the laspeyres price index and what's its formula?
Quantities at base period levels are held constant.
175
What's the formula for laspeyres quantity index?
176
What are index numbers based off and what's their weakness?
Index numbers are generally based in samples of items. The problem with that is there's room for sampling errors. Also factors like technological changes, product quality changes, and changes in consumer purchasing patterns can individually and collectively make comparisons over time unreliable.
177
What's the Paasche Index?
Makes use of a weighted aggregate index which uses current time period weights, which is useful for continuously changing goods. It's more accurate than the laspeyres's index as it reflects what the industry is actually using in the current year, and therefore takes account of the price changes and the quantity changes.
178
What's Paasche index's formula?
179
What's Paasche index's formula?
-
Key Links
-
Subjects
-
Company
-
Find Us
-
