descriptive statistics (A)

Question 1

what is meant by descriptive statistics?

Answer 1

Descriptive statistics are brief descriptive coefficients that summarize a given data set, which can be either a representation of the entire or a sample of a population.

Question 2

what is descriptive statistics are involved with this set?

Answer 2

• measure of central tendency

- measures of spread (dispersion)

Question 3

what are the measures of central tendency?

Answer 3

• mean / average
• mode / popular
• median / middle

Question 4

what are the measures of dispersion?

Answer 4

• range
• IQR
• Sandard deviation

Question 5

what is meant by measures of central tendency?

Answer 5

term term average is used in everyday life ro express an amount that is typical for a group of people / things

typical tendency of groups

measures of CT is a single value that attempts to describe a set of data by identifying the central position in data set

Question 6

why is average useful?

Answer 6

useful indicator of the general trend

• summarise large amounts of data
• indicate that there is some variability around the single value within original data

Question 7

what are the pros of the mean?

Answer 7

• most popular measure
• yields one distinct answer
• useful for comparing data sets

Question 8

what are the cons of the mean/

Answer 8

• answer can be affected by extreme values (outliers) or when skewed data is present
• mean has tendency to be pulled towards extreme values

Question 9

what are the pros of the median?

Answer 9

• unaffected by extreme values

- if there is skewed data it may be more informative decriptce measure then the mean

Question 10

what are the cons of the median?

Answer 10

• less amenable then the mean

Question 11

what ate the pros of them doe?

Answer 11

• easy to obtain

- only measure that can used for data on nominal scale

Question 12

what are the cons of the mode?

Answer 12

• it is not very stable from sample to sample

- there may be more than one mode for a particular score

Question 13

what is non skewed data?

Answer 13

equal (perfect distribution)

mean is preferred

Question 14

what is skewed data?

Answer 14

large amounts of outliers

median is less affected by skewed dat and id generally considered to be the best

Question 15

when do you use the mode?

Answer 15

for nominal data

Question 16

when do you use the median?

Answer 16

ordinal

interval/ration (skewed)

Question 17

when do you use the mean?

Answer 17

interval/ratio (non skewed)

Question 18

what are measures of spread?

Answer 18

describe how similar or varied the set of observed values are for a particular variable

large spread = large differences
seen as positive if there is little deviation

Question 19

what are the types of measures of spread?

Answer 19

• range
• quatiles
• deviation (absolute deviation, variance, standard deviation)

Question 20

what are the types of deviation?

Answer 20

absolute deviation, variance and standard deviation

Question 21

what is the range?

Answer 21

difference between the highest and the lowest variable

Question 22

what are the pros of range?

Answer 22

• useful when measuring variable with a critical low/high threshold that should not be crossed e.g. drinking age
• easy

Question 23

what are the cons of the range?

Answer 23

• value is sensitive to outliers

Question 24

what are quartiles?

Answer 24

tell us about the spread of data set by breaking data set into quarters, just as the median breaks in half

Question 25

how many quartiles are there?

Answer 25

Q1 Q2 Q3

Question 26

how do you work out the quartiles?

Answer 26

- if you find the median you will find Q2 | - then work out the median of the number outside to find Q2 and 3

Question 27

what is the interquartile range?

Answer 27

the difference between 1st and 3rd quartile IQR = Q3 - Q1

Question 28

what is a box plot?

Answer 28

visual description of the distribution based on minimum Q1, median, Q3, maximum

Question 29

what is an outlier?

Answer 29

observation which does not appear to belong with other data (measurement or recording error / equipment failure) have to find them as can skew the data

Question 30

how do you find outliers?

Answer 30

Q1-1.5 x IQR Q3+1.5 x IQR anything outside of these fences is considered an outlier

Question 31

what is the disadvantage to quartiles?

Answer 31

does not take into account every score just 25%

Question 32

what is the difference between mean absolute deviation and standard?

Answer 32

both looking at the distance of the data oto its mean standard is calculating the square of the difference absolute is only looking at the absolute difference

Question 33

how do yo work out mean absolute deviation?

Answer 33

- find the mean of all values - find the distance of each value from that mean, subtract mean from each value, ignore minus) - find the mean of those distances SUM OF (x-u) / N ``` x = each value u = mean n = number of values ```

Question 34

what is the variance?

Answer 34

the average of the squared differences from the mean

Question 35

how do you calculate the variance?

Answer 35

- work out the mean - for each number subtract the mean and square the result - the work out the average of those squared differences (but minus one) SUM OF (x-u)2 / n-1

Question 36

why do you use n-1 for standard deviation and variance?

Answer 36

to overcome bias

Question 37

what are the problems with sample variance?

Answer 37

- as they are squared this gives more weight to extreme scores - it contains outliers, variance ay not represent data as a whole - not same units as data (unit squared) cannot directly relate

Question 38

wat is standard deviation?

Answer 38

measure of spread of scores within data set use in conjunction with mean to summarise continuous data - normally apparopraite if data not skewed or has outliers

Question 39

how do you work out standard deviation

Answer 39

``` (square root of variance) work out mean subtract mean and quare add all square find mean of those squared find square root ```