Measures of variability

Question 1

Measures of central tendency

Answer 1

Summarises a data set with a single value that is representative of the data set

Question 2

What has to happen for data to be approximately equal?

Answer 2

The mean, median and mode will all be the same

Question 3

What is variability

Answer 3

• The extent to which things are not all the same

- How scores differ from one another

Question 4

The two major roles of variability?

Answer 4

1. Inferential statistics

2. Descriptive statistics

Question 5

Inferential statistics

Answer 5

The amount of variability affects the kind of statements we can make about our population and the degree of confidence we can have in those statements

Question 6

Descriptive statistics

Answer 6

Variability is an interesting property of a data set in itself - trying to understand the data itself

Question 7

Low variability

Answer 7

The shape of the distribution is low so a lot of the values cluster around the narrow peak, not a lot of spread

Question 8

High variability

Answer 8

Much broader tail, more scores distributed over the data set

Question 9

Numerical measurements of variability - The range

Answer 9

Largest score minus the smallest score - all values can be found within this range - but not very accurate

Question 10

Possibility for making the range more accurate

Answer 10

• Look at the difference of each score in the distribution from the mean
• Add the differences up and divide by the number of the scores to get the mean deviation

Question 11

The mean deviation

Answer 11

(xi - x) / n - mean deviation

Mean deviation always sums to 0

Question 12

Numerical measurements of variability - the variance (s2)

Answer 12

(xi - x)2 / n - The sum of the squared deviation from the mean deviation by the number of scores

Question 13

Measure of variability in the original units of measurement - standard deviation

Answer 13

Take square root of the variance - square root of (xi - x)2 / n

Question 14

What is the SD?

Answer 14

Approximately the average distance of the scores in a data set from the mean - most useful measure of variability

Question 15

Inflection point

Answer 15

Point where the curve starts bending outward more, always 1 standard deviation from the mean

Question 16

The z-score formula

Answer 16

z = xi - x(bar) / s

Question 17

what does the z-score tell us?

Answer 17

How far away a score is from the mean, taking into account the variability of the scores in the data set

Question 18

The z-score allows us to interpret score in terms of…?

Answer 18

• Relative standing (x) from the mean

- Variability (s) in the distribution by comparing with the standard normal curve

Question 19

Relative frequency or proportion of cases between two values…

Answer 19

Area under the normal distribution curve bounded by two values

Question 20

What can be determined by comparing z with standard normal

Answer 20

Can determine what proportion of scores are less than or greater than the individual score

Question 21

How to give a clear picture of where scores sit…

Answer 21

1. Calculate z-score
2. Draw a picture
3. Look up value of z in z-table to find the relative position of xi

Question 22

What is a z-table?

Answer 22

It tells us what proportion of values above and below that specific z-value is

Question 23

properties of the z-distribution

Answer 23

1. it isn normal
2. x = 0
3. s = 1

Question 24

z-scores are used (as descriptive) to…

Answer 24

1. Find the relative position of a data element in its distribution
2. Allow comparisons between scores from different distributions

Question 25

Comparing scores from different distributions

Answer 25

Different distributions may vary in both their mean and SD which makes comparing across different distributions difficult