The median of the following frequency distribution is $525$ . Find the values of missing frequencies $x$ and $y$ , if the total frequency is $100$ . Class interval | Frequency 0–100 | 2 100–200 | 5 200–300 | x 300–400 | 12 400–500 | 17 500–600 | 20 600–700 | y 700–800 | 9 800–900 | 7 900–1000 | 4

hard 5 marks Class 10 · Mathematics · Statistics

Answer

x = 9, y = 15

The correct answer is x = 9, y = 15 — Substitute $x = 9$ into Equation 1: $9 + y = 24 ⟹ y = 15$ .

Step-by-step solution

Sum of all frequencies equals $100$ : $2 + 5 + x + 12 + 17 + 20 + y + 9 + 7 + 4 = 100$ .
Simplify the sum: $76 + x + y = 100 ⟹ x + y = 24$ (Equation 1).
Given Median $= 525$ , which lies in the class interval $500 - 600$ . Thus, $500 - 600$ is the median class.
Identify the required values: $l = 500$ , $f = 20$ , $h = 100$ , $\frac{N}{2} = 50$ , and cumulative frequency of preceding class $c f = 2 + 5 + x + 12 + 17 = 36 + x$ .
Use the median formula: $Median = l + (\frac{\frac{N}{2} - c f}{f}) \times h$ .
Substitute values: $525 = 500 + (\frac{50 - ( 36 + x )}{20}) \times 100$ .
Simplify the equation: $25 = (14 - x) \times 5 ⟹ 14 - x = 5 ⟹ x = 9$ .
Substitute $x = 9$ into Equation 1: $9 + y = 24 ⟹ y = 15$ .

Common mistake: Forgetting to put parentheses around

(36 + x)

when subtracting

c f

, leading to sign errors.

Concept tested: Finding missing frequencies using median