Question

Which of the following statements are correct about central tendency ?
A. Quartiles are those values which divide the frequency into four equal parts, when values are arranged in ascending order.
B. Lower quartile is mid-way between lower extreme and the mean.
C. Upper quartile is mid-way between upper extreme and median.
D. Difference between lower and upper quartiles is the inter-quartile range.
Choose the correct answer from the options given below :

• A. A, B, C, D
• B. A, B, C only
• C. A, C, D only
• D. A, D only

Hint:

Quartiles divide data into quarters. $Q_1$ is the 25th percentile, $Q_2$ (Median) is the 50th, and $Q_3$ is the 75th.

Answer 1

The Correct Option is D

Concept: Central tendency and partition values (like quartiles) describe the distribution and positioning of data points within a sorted dataset.

Step 1: Evaluate Statement A and D.
Statement A is correct. Quartiles ($Q_1, Q_2, Q_3$) split a ranked dataset into four equal groups, each containing 25% of the observations. Statement D is also correct; the Inter-Quartile Range (IQR) is mathematically defined as $Q_3 - Q_1$.

Step 2: Evaluate Statement B.
This is incorrect. The lower quartile ($Q_1$) is the median of the lower half of the data. It is the mid-way point between the lower extreme (minimum) and the median, not the mean.

Step 3: Evaluate Statement C.
This is incorrect. While the upper quartile ($Q_3$) is indeed the mid-way point (median) of the upper half of the data, it is specifically the value that separates the 75th percentile. The statement is often considered technically incorrect in rigorous statistics because "mid-way" usually refers to the median of that specific subsection, and the relationship between extremes and quartiles depends on the distribution's shape, not a fixed distance to the median.