Identify the median class. Class 0–5: 2, 5–10: 12, 10–15: 6, 15–20: 5, 20–25: 5.

Class 10StatisticsStatistics and Probability

A5–10
B10–15
C15–20
D0–5

Step-by-Step Solution

n = 30, so n/2 = 15. The cumulative frequencies are 2, 14, 20, 25, 30 and the first one to reach 15 is 20, in the class 10–15. Note that 5–10 has the highest frequency (12) — that makes it the MODAL class, not the median class.

Answer: B) 10–15

Key idea: Mode for grouped data

**Modal class**: class with HIGHEST frequency.

**Mode formula**:
**Mode =

l + h \times (f

₁ −

f

₀) /

(2 f

₁ −

f

₀ −

f

₂)**

Where:
-

l

= lower limit of modal class
-

h

= class width
-

f

₁ = frequency of modal class
-

f

₀ = frequency of class BEFORE modal class
-

f

₂ = frequency of class AFTER modal class

**Example**: Modal class 30–40 with

f

₁ = 12,

f

₀ = 5,

f

₂ = 8.

l = 30, h = 10

.
Mode =

30 + 10 \times (12 - 5) / (24 - 5 - 8) = 30 + \frac{70}{11}

≈ 36.36.

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