Lesson 5 Measures of variability

Question 1

• Are measures of the average distance of each observation from the center of the distribution.
• They measure the homogeneity or heterogeneity of a particular group

Answer 1

Measures of variability or dispersion

Question 2

A small measure of variability would indicate that the data are:

Answer 2

1. clustered closely around the mean
2. more homogeneous
3. less variable
4. more consistent
5. more uniformly distributed.

Question 3

Measures of Variability or Dispersion

Answer 3

Range (R)
Mean Absolute Deviation (MAD)
Variance (σ ², s ²)
Standard Deviation (σ, s)
Coefficient of Variation (cv)

Question 4

This is the simplest but the most unreliable measure of variability since it uses only two values in the distribution

Answer 4

Range (R)

Question 5

Disadvantages of Range

Answer 5

1. For a very large sample, it is an unstable descriptive measure of dispersion.
2. Since only two values are used in the computation, the range is an unreliable measure of dispersion.
3. The range of two sets of data composed of different numbers of samples are not directly comparable

Question 6

is the simplest measure of variability that takes into account all data in the distribution

Answer 6

Mean Absolute Deviation (MAD)

Question 7

Disadvantages of MAD

Answer 7

1. Since the mean is used in its computations, then it is also greatly affected by extreme values
2. Its use in further statistical computation is very limited
3. It is not amenable to algebraic manipulation because of the use of absolute values.

Question 8

are both reliable measures of variability or spread of the distribution

However, we cannot use them in comparing two sets of data of different units

Answer 8

SD and Variance

Question 9

is the ratio of the standard deviation to the mean.

It is used to compare the variability of two or more sets of data even when they are expressed in different units of measurement.

Answer 9

Coefficient of variation (cv)

Question 10

is the square root of the average deviation from the mean, or simply the square root of the variance.

Answer 10

Standard Deviation

Question 11

is the average of the squares of the differences between the individual (observed) and the expected value

Answer 11

Variance

Question 12

is a distribution with a bell-shaped appearance.

Answer 12

Normal distribution

Question 13

refers to the degree of symmetry or asymmetry of a distribution

Answer 13

Skewness

Question 14

If a distribution is skewed to the left

Answer 14

mean is less than its median
(mean < median)
negatively skewed

Question 15

If a distribution is skewed to the right

Answer 15

mean is greater than its median
(mean > median)
positively skewed

Question 16

The extent of skewness can be obtained by getting the

Answer 16

coefficient of skewness

Question 17

SK = 0

Answer 17

distribution is NORMAL

Question 18

SK < 0

Answer 18

distribution is SKEWED to the LEFT

Question 19

SK > 0

Answer 19

distribution is SKEWED to the RIGHT

Question 20

refers to the peakedness or flatness of a distribution

Answer 20

Kurtosis

Question 21

Kurtosis

is a normal distribution

Answer 21

Mesokurtic

Question 22

Kurtosis

is more peaked than the normal distribution.

Answer 22

Leptokurtic

Question 23

Kurtosis

is flatter than the normal distribution.

Answer 23

Platykurtic

Question 24

Ku > 3

Answer 24

Leptokurtic

Question 25

Ku < 3

Answer 25

Platykurtic

Question 26

Ku = 3

Answer 26

Mesokurtic