Find the modal class: marks 0–20:7, 20–40:14, 40–60:22, 60–80:22, 80–100:5. (Two classes tie for highest frequency.) Which statement is correct?

Class 10StatisticsStatistics and Probability

Step-by-Step Solution

Both 40–60 and 60–80 have the highest frequency 22, so the data has two modal classes (bimodal).

Answer: A) The distribution is bimodal with modal classes 40–60 and 60–80.

**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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