Chapter 4- Variability

Question 1

Variability

Answer 1

Having a range of values

It is the quantitative measure of the degree to which scores in a distribution are spread out or clustered together

Question 2

Range

Answer 2

Highest score minus the lowest score

Question 3

Interquartile Range

Answer 3

Range of scores that contains the middle 50% of a distribution
This is an important element of box plots

To find the IQR, you must find two different percentiles, the 25th and 75th. You subtract 75th- 25th

Ex. 0.25 x N, your answer is what place a score is. Like, if your answer was 10 then it would be the tenth number .

To find a semi- IQR- Take (75th-25th)/2

Question 4

Standard Deviation

Answer 4

Descriptive measure of the dispersion of scores around the mean
It provides us with the width of the distribution

There are three different kinds of SD variability:
Lowercase sigma, S hat, and capital S

Standard deviation is the square root of variance

Question 5

Deviation score formula

Answer 5

Shows clearly how each score contributes to the final result

Question 6

Deviation score

Answer 6

Raw score minus the mean of is distribution

Tells us the number of points that a particular score deviates from, or differs from, the mean

Ex. If we got -5, we were -5 below the mean

Question 7

Lowercase sigma

Answer 7

Measure of a population’s variability. A parameter. Describes variability when a population of data is available

Lowercase sigma and capital S have the same equation

Question 8

S hat

Answer 8

Estimate of a population’s variability. A statistic. An estimate of lowercase sigma (in the same way that X bar is an estimate of mu). The variability statistic you will use most often in this book.

A hat on a symbol indicates that something is being estimated.
Note that the difference between S and lowercase sigma is that S hat has N-1 in its denominator because it IS AN ESTIMATE

Question 9

Capital S

Answer 9

Measure of sample variability. Describes the variability of a sample when there is no interest in estimating lowercase sigma (which is the measure of a population’s variability)

Question 10

Variance

Answer 10

Square of the standard deviation.

It is the standard deviation equation, before you take the square root of it. Variance is not very useful in descriptive statistics, but is in inferential statistics

Question 11

What is considered an extreme score when talking about SDs and variability?

Answer 11

1. More than 2sd above
2. More than 2sd below
3. Unrealistically large
4. Unrealistically small

Question 12

What factors can affect variability?

Answer 12

1. Extreme scores (range is the most affected, IQR is the least)
2. Sample size (range is the most affected, sd/variance/IQR are least)
3. Sampling stability (range least reliable, sd/variance/IQR tend to be similar
4. Open-ended distributions (sd/variance/range cannot be computed, only IQR can be estimated)