Measures of variability

Question 1

What are the measures of variability?

Answer 1

1. Range
2. Inter-quartile range (IQR)
3. Variance (VAR)
4. Standard deviation (SD)

Question 2

What is the range?

Answer 2

Range= highest score - lowest score
- measure of variation in interval-ratio variables
- difference between highest and lowest scores in distribution

Question 3

What is the Interquartile range?

Answer 3

• measure of variation for interval-ratio data
• indicates the width of the middle 50% of the distribution and is defined as the difference between the lower and upper quartiles (Q1 and Q3)
  IQR= Q3 ( 75th percentile) - Q1 (25th percentile)

Question 4

What is the box plot?

Answer 4

graphic device that visually presents: range, IQR, median, quartiles, minimum and maximum values

Question 5

What are the following entities?
1. (x - x̄)
2. (x - x̄)²
3. å (x- x̄)²
4. å (x- x̄)² / N
5. √å (x- x̄)² / N

Answer 5

(x - x̄) the deviation between the mean and one observation
(x - x̄)² the squared deviation
å (x- x̄)² sum of squared deviations
å (x- x̄)² / N the average of squared deviations, or variance adjusting for N-1
√å (x- x̄)² / N the square root of squared deviations or standard deviation without adjusting for N-1

Question 6

What is variance?

Answer 6

• a measure of variation for interval-ratio variables
• the average of the squared deviations from the mean

Question 7

What is standard deviation?

Answer 7

• measure of variation for interval-ratio variables
• equal to the square root of the variance

Question 8

Why do we need the sum of squared deviations instead of the sum of deviations to denote variability?

Answer 8

because the sum of deviations is always 0 and we need to accumulate non-negative entities

Question 9

Why do we need to divide the sum of squared deviations by N?

Answer 9

To get rid of the influence of sample sizes

Question 10

Why do we need to take the square root of the variance and call it standard deviation?

Answer 10

to roll back the “squared” deviations