Question

Which of the following are the measures of variability?
A. Mode
B. Quartile
C. Percentile
D. Range
E. Standard deviation
Choose the correct answer from the options given below:

• A. A & amp; D Only
• B. B & amp; C Only
• C. C & amp; D Only
• D. D & amp; E Only

Hint:

Remember the three classic statistical groups:
1. Central Tendency: Mean, Median, Mode.
2. Partition/Position: Quartiles, Deciles, Percentiles.
3. Dispersion/Variability: Range, Standard Deviation, Variance, Mean Deviation.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question requires us to identify statistical measures of variability (or dispersion) from the provided list.

Step 2: Key Formula or Approach:
Descriptive statistics are classified into three major groups: measures of central tendency, measures of position (or partition), and measures of variability (dispersion).

Step 3: Detailed Explanation:

• Let us analyze each statistical measure:

• A. Mode: A measure of central tendency representing the value that appears most frequently in a data set.

• B. Quartile: A measure of position that divides a sorted data set into four equal parts.

• C. Percentile: A measure of position indicating the relative position of a score within a group of 100 parts.

• D. Range: A measure of variability defined as the difference between the maximum and minimum values in a data set:
\[ \text{Range} = X_{\text{max}} - X_{\text{min}} \]

• E. Standard deviation: A measure of variability representing the average deviation of scores from the mean:
\[ \sigma = \sqrt{\frac{\sum (X_i - \mu)^2}{N}} \]

• Therefore, Range (D) and Standard deviation (E) are the correct measures of variability.

Step 4: Final Answer:
The correct option is D & amp; E Only, which corresponds to Option (D).