Statistics
Mean Deviation about Median — Frequency Distribution
nta_pyq_2024_apr
Grade 11
Question:
The frequency distribution of the age of students in a class of 40 students is given below.
| Age | 15 | 16 | 17 | 18 | 19 | 20 |
|---|---|---|---|---|---|---|
| No of Students | 5 | 8 | 5 | 12 | $x$ | $y$ |
If the mean deviation about the median is 1.25, then $4x+5y$ is equal to:
Step-by-Step Solution
Key Concept: $x+y=10$ (total = 40). Median $=18$ (cumulative: 5,13,18,30 — the 20th observation falls at age 18). M.D. $=\frac{\sum f_i|x_i-M|}{40}=1.25\Rightarrow\sum f_i|x_i-18|=50$.
$x=6,y=4$. $4x+5y=44$.
Correct Answer: 3