LECTURE 5

Question 1

What is dispersion?

Answer 1

The spread or variation of data points around a central value.

Question 2

What is the purpose of dispersion?

Answer 2

To measure the variability of data and provide a complete picture beyond averages.

Question 3

What are the characteristics of a good measure of dispersion?

Answer 3

1. Rigidly defined 2. Based on all observations 3. Not affected by extreme values 4. Allows algebraic manipulation 5. Simple to calculate and understand.

Question 4

What is the range?

Answer 4

The difference between the largest and smallest values in a dataset.

Question 5

What is the formula for range?

Answer 5

Range = L - S, where L is the largest value and S is the smallest value.

Question 6

What is the range for continuous data using Method 1?

Answer 6

L = Upper boundary of the highest class, S = Lower boundary of the lowest class.

Question 7

What is the range for continuous data using Method 2?

Answer 7

L = Midpoint of the highest class, S = Midpoint of the lowest class.

Question 8

What are the merits of range?

Answer 8

1. Simple to calculate 2. Easy to understand 3. Useful in quality control, weather forecasts, and stock analysis.

Question 9

What are the demerits of range?

Answer 9

1. Affected by extreme values 2. Based on only two observations 3. Not suitable for open-end intervals 4. Rarely used as a standalone measure.

Question 10

What is standard deviation (SD)?

Answer 10

The positive square root of the arithmetic mean of squared deviations from the mean.

Question 11

What is the formula for standard deviation for raw data?

Answer 11

s = √[Σ(x - x̄)² / n].

Question 12

What is the formula for standard deviation for grouped data (discrete)?

Answer 12

s = √[Σf(x - x̄)² / n].

Question 13

What is the formula for standard deviation for grouped data (continuous)?

Answer 13

s = √[Σf(d²) / n - (Σf(d) / n)²], where d = x - A.

Question 14

What are the merits of standard deviation?

Answer 14

1. Rigidly defined 2. Uses all observations 3. Suitable for mathematical analysis 4. Less affected by sampling fluctuations.

Question 15

What are the demerits of standard deviation?

Answer 15

1. Difficult to compute 2. Gives more weight to extreme values 3. Cannot be used for direct comparisons.

Question 16

What is variance?

Answer 16

The square of the standard deviation.

Question 17

What is the formula for variance?

Answer 17

Variance = (SD)².

Question 18

What is the coefficient of variation (CV)?

Answer 18

A relative measure of dispersion expressed as a percentage.

Question 19

What is the formula for coefficient of variation (CV)?

Answer 19

CV = (SD / Mean) × 100.

Question 20

What is the purpose of CV?

Answer 20

To compare variability between datasets with different units.

Question 21

What is an example of using CV for comparison?

Answer 21

If CV for yield is 20% and for plant height is 9.1%, yield is more variable.

Question 22

Which measure is affected most by extreme values?

Answer 22

Standard Deviation.

Question 23

Variance is the square of which measure?

Answer 23

Standard Deviation.

Question 24

If CV of Variety I is 30% and Variety II is 25%, which is more consistent?

Answer 24

Variety II.

Question 25

For the dataset 5, 5, 5, 5, 5, 5, what is the standard deviation?

Answer 25

0

Question 26

Do absolute measures of dispersion have the original units?

Answer 26

Yes.

Question 27

Can the mean deviation value for a dataset be negative?

Answer 27

No.

Question 28

Define dispersion.

Answer 28

The spread or variation of observations from their central value.

Question 29

Define CV and its uses.

Answer 29

CV is the ratio of SD to the mean expressed as a percentage. It compares variability between datasets with different units.

Question 30

What are the differences between absolute and relative measures of dispersion?

Answer 30

1. Absolute measures have the same units as the data (e.g., Range, SD). 2. Relative measures (e.g., CV) are unitless and expressed in percentages.

Question 31

How is standard deviation calculated for raw data?

Answer 31

Using the formula: s = √[Σ(x - x̄)² / n].

Question 32

How is standard deviation calculated for grouped data?

Answer 32

Using the formula: s = √[Σf(d²) / n - (Σf(d) / n)²], where d = x - A.