CRP 109 Stats Lecture 1

Question 1

Data definition

Answer 1

Collections of observations, such as measurements, or survey
responses

Question 2

Statistics definition

Answer 2

The science of planning studies and experiments; obtaining data; and organizing, summarizing, presenting, analyzing, and interpreting those data and then drawing conclusions
based on them

Question 3

Population definition

Answer 3

The complete collection of all measurements or data that are
being considered. Typically, it is the complete collection of data that we would like to make inferences about

Question 4

Census definition

Answer 4

The collection of data from every member of the population

Question 5

Sample definition

Answer 5

The subcollection of members selected from a population

Question 6

Variable definition

Answer 6

A characteristic that varies (changes) across individuals in a
population. The values (observations) recorded collectively
make up the data

Question 7

parameter definition

Answer 7

A numerical measurement describing some characteristic of a
population

Question 8

statistic definition

Answer 8

A numerical measurement describing some characteristic of a
sample

Question 9

Discrete data

Answer 9

result when the data values are quantitative and the number of
values is finite (countable)

Question 10

Continuous data

Answer 10

result from infinitely many possible quantitative values
(not countable). They can be measured, but not counted.

Question 11

Missing completely at random

Answer 11

The likelihood of the data value being
missing is independent of its value or any of the other values in
the data set (any data value is just as likely to be missing as
any other data value)

Question 12

Missing not at random

Answer 12

The missing value is related to the reason that it is missing. Ignoring these could lead to bias in the remaining
values and the results may then become misleading

Question 13

Simple random sample (SRS)

Answer 13

A sample of n subjects selected in such a way that every possible sample of the same size n has the
same chance of being chosen

Question 14

Designed Experiment

Answer 14

We apply some treatment and then proceed to observe its effects on the individuals. The individuals in
designed experiments are called experimental units, and they
are often called subjects when they are people

Question 15

Observational Study

Answer 15

We observe and measure specific characteristics, but
we do not attempt to modify the individuals being studied

Question 16

Random Sampling Error

Answer 16

Occurs when the sample has been selected with a
random method, but there is a discrepancy between a sample
result and the true population result; such an error results from
chance sample fluctuations

Question 17

Non-Sampling Error

Answer 17

The result of human error, including such factors as wrong data entries, computing errors, questions with biased wording, false data provided by respondents, forming biased
conclusions, or applying statistical methods that are not
appropriate for the circumstances

Question 18

Non-Random Sampling Error

Answer 18

The result of using a sampling method that is not random, such as using a convenience sample or a
voluntary response sample

Question 19

Frequency (of a class)

Answer 19

The number of original values that fall into that class.

Question 20

Frequency Distribution/Table

Answer 20

Shows how data are partitioned among
several categories/classes by listing the categories along with
the number (frequency) of data values in each of them
-used to summarize large data sets, see the distribution and identify outliers, and/or have a basis for constructing
graphs.

Question 21

Lower Class Limits

Answer 21

The smallest numbers that can belong to each of the
different classes

Question 22

Upper Class Limits

Answer 22

The largest numbers that can belong to each of the
different classes

Question 23

Class Boundaries

Answer 23

The numbers used to separate the classes, but without
the gaps created by class limits.

Question 24

Class Midpoints

Answer 24

The values in the middle of the classes. Each class midpoint
is computed by taking the average of the lower and upper class
limits

Question 25

Class Width

Answer 25

The difference between two consecutive lower class limits (or boundaries) in a frequency distribution. class width = (max value - min value) / number of classes

Question 26

Relative (or Percentage) Frequency Distribution

Answer 26

relative freq = freq of class / sum of all freq *100 to get percentage freq

Question 27

Cumulative Frequency Distribution

Answer 27

frequency for each class is the sum of the frequencies for that class and all previous classes - class limits are replaced by “less than” expressions that describe the new ranges of values

Question 28

Histogram

Answer 28

A graph consisting of bars of equal width drawn adjacent to each other (unless there are gaps in the data). The horizontal scale represents classes of quantitative data values, and the vertical scale represents frequencies. The heights of the bars correspond to frequency values.

Question 29

Relative Frequency Histogram

Answer 29

A graph that has the same shape and horizontal scale as a histogram, but the vertical scale uses relative frequencies instead of actual frequencies (i.e. proportion or percent)

Question 30

Correlation

Answer 30

Exists between two variables when the values of one variable are somehow associated with the values of the other variable. Correlation does not imply causation.

Question 31

Linear Correlation

Answer 31

Exists between two variables when there is a correlation and the plotted points of paired data result in a pattern that can be approximated by a straight line

Question 32

Linear Correlation Coefficient, r

Answer 32

Measures the strength of the linear correlation between the paired quantitative x and y values in a sample. It is sometimes referred to as the Pearson product moment correlation coefficient

Question 33

Scatterplot

Answer 33

A plot of paired (x , y ) quantitative data with a horizontal x -axis and a vertical y -axis

Question 34

Properties of r

Answer 34

-The value is always between −1 and 1, inclusive -If r is close to −1, there appears to be a strong negative correlation. -If r is close to 1, there appears to be a strong positive correlation. -If r is close to 0, there appears to be a weak or no linear correlation. -A value of exactly −1 or 1 implies that all of the data fall exactly on a line (perfect correlation) -If all values of either variable are converted to a different scale, the value of r does not change - Interchange all x values and y values, and the value of r will not change - not designed to measure the strength of a relationship that is not linear -sensitive to outliers

Question 35

Regression

Answer 35

Given a collection of paired sample data, the regression line or line of best fit or least-squares line is the straight line that “best” fits the scatterplot of the data

Question 36

Descriptive Statistics

Answer 36

Methods and tools that summarize or describe relevant characteristics of data

Question 37

Inferential Statistics

Answer 37

Methods and tools that make inferences, or generalizations, about populations

Question 38

Mean

Answer 38

The measure of centre found by adding all of the data values and dividing the total by the number of data values -not resistant to outliers

Question 39

Median

Answer 39

The measure of centre that is the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude. -resistant to outliers (only changes slightly)

Question 40

Mode

Answer 40

-The value(s) that occurs with the greatest frequency. -The mode can be found with qualitative data. -A data set can have no mode, one mode (unimodal), or multiple modes

Question 41

s

Answer 41

sample standard deviation

Question 42

s2

Answer 42

sample variance

Question 43

σ

Answer 43

population standard deviation

Question 44

σ2

Answer 44

population variance

Question 45

Range

Answer 45

-The difference between the maximum data value and the minimum data value -Very sensitive to outliers (not resistant) - does not truly reflect the variation among all of the data values

Question 46

Standard Deviation of a Sample (s)

Answer 46

A measure of how much data values deviate away from the mean T-he value is never negative. It is zero only when all of the data values are exactly the same. -Larger values indicate greater amounts of variation. -not resistant to outliers - units are the same as the units of the original data values

Question 47

Variance

Answer 47

-A measure of variation equal to the square of the standard deviation. -The units are the squares of the units of the original data values -not resistant to outliers -The value is never negative. It is zero only when all of the data values are the same number. -s2 is an unbiased estimator of σ2

Question 48

Chebychev’s Rule

Answer 48

for any data set: -at least 75% of data lies within 2 standard deviations of the mean. -at least 89% of data lies within 3 standard deviations of the mean

Question 49

Empirical Rule

Answer 49

The empirical rule states that for bell-shaped data sets, -approximately 68% of data lies within 1 standard deviation of the mean. -approximately 95% of data lies within 2 standard deviations of the mean. -approximately 99.7% of data lies within 3 standard deviations of the mean

Question 50

Percentiles

Answer 50

Measures of location, denoted P1, P2, . . . , P99, which divide a set of data into 100 groups with about 1% of the values in each group -The 50th percentile, P50, has about 50% of the data values below it and about 50% of the data values above it, corresponding to the median

Question 51

Finding the Percentile of a Data Value

Answer 51

percentile of value x = (number of values less than x) / (total number of values) *100

Question 52

k

Answer 52

percentile being used

Question 53

L

Answer 53

locator that gives the position of a value in a sorted list

Question 54

Pk

Answer 54

kth percentile

Question 55

Converting a Percentile to a Data Value

Answer 55

1. arrange values lowest to highest 2. L = (k/100)n 3. if L whole number, kth percentile is midway between Lth value and the next value in the sorted set of data. i.e. Pk = (Lth value + next value) / 2 4. if L is not whole number, round L up. Pk is the Lth value counting from the lowest in the data set.

Question 56

Quartiles

Answer 56

Measures of location, denoted Q1, Q2, and Q3 which divide a set of data into four groups with about 25% of the values in each group Q1 = P25 Q2 = P50 Q3 = P75

Question 57

Interquartile range (IQR)

Answer 57

(IQR) = Q3 − Q1 -another measure of spread that is less sensitive to outliers

Question 58

5-Number Summary

Answer 58

For a set of data, consists of these five values: 1. Minimum 2. First quartile, Q1 3. Second quartile, Q2 (same as the median) 4. Third quartile, Q3 5. Maximum

Question 59

Constructing a Boxplot

Answer 59

Can be used to identify skewness 1. Find the 5-number summary. 2. Construct a line segment extending from the minimum data value to the maximum data value. 3. Construct a box (rectangle) extending from Q1 to Q3, and draw a line in the box at the median.

Question 60

Identifying Outliers for Modified Boxplots

Answer 60

1. Find the quartiles. 2. Find the IQR. 3. Evaluate 1.5×IQR. 4. In a modified boxplot, a data value is an outlier if it is: above Q3 by an amount greater than 1.5×IQR; or below Q1 by an amount greater than 1.5×IQR. -A special symbol (such as an asterisk or point) is used to identify outliers as defined previously. -The solid horizontal line extends only as far as the minimum data value that is not an outlier and the maximum data value that is not an outlier