Unit 6: Measures of Variability

Question 1

• Variability, also referred to as dispersion

Answer 1

indicates how much
individual cases tend to deviate from what is typical in the data

Question 2

If scores are very similar, little or low dispersion

Answer 2

homogeneous

Question 3

Measures of Variability

Answer 3

• Range
• Interquartile Range
• (Semi-interquartile Range)
• Standard Deviation and Variance

Question 4

• If scores are very different, high degree of dispersion.

Answer 4

heterogeneous

Question 5

Range

Answer 5

The distance from the largest to the smallest number.
* Example: test scores: 70 83 83 83 90 90 94 95 95
* The range is calculated by subtracting the smallest value (70) from the largest
value (95): R = 25

Question 6

Quartiles = Q

Answer 6

The 1st quartile (Q1) is the point below which 25% of the scores occur (P25).

• The 2nd quartile (Q2) is the point below which 50% of the scores occur
  (P50). It is also the median.
• The third quartile (Q3) is the point below which 75% of the scores occur (P75)
• These points in the distribution are arbitrary.
• Sometimes people are interested in deciles (every 10% of the distribution)

Question 7

boxplot

Answer 7

Question 8

The Violin
Plot

Answer 8

• Alternative to box plot
• a smoothed version of the histogram
• The violin plot places a
  simple version of a
  boxplot (median, box) in
  the center

Question 9

Measure of spread: standard deviation

Answer 9

The standard deviation is used to describe the variation around the mean.
Like the mean, it is not resistant to outliers

1. First calculate the variance s
2. Then take the square root to get
   the standard deviation s.

Question 10

How to Calculate the Quartiles and the Interquartile Range

Answer 10

Question 11

types of graphs

Answer 11

Question 12

variance s^2

Answer 12

how far a set of (random) numbers are
spread out from their average value

Question 13

standard deviation s

Answer 13

describes the variation
around the mean (how spread out the
data are from the mean

Question 14

Calculating the Variance

Answer 14

Difference between individual score and the mean

Square the differences

Sum the squared differences

Divide by number of observations – 1

Question 15

Samples usually over or under estimate the amount of variation in a population

Answer 15

underestimate

• Dividing by n-1 instead of n is a correction for this

Question 16

From Variance to Standard Deviation

Answer 16

Difference between individual score and the mean
Square the differences
Sum the squared differences
Divide by number of observations – 1
Take the square root of variance to get SD