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Statistics
CBSE 2026 Board Exam Set 1 (Code 30/7/1)
CBSE_BOARD_PYQ_2026_30_7_1
Grade 10
Question:
[Section D]
Find the mean and mode of the frequency distribution of daily wages of workers shown in the given table.
Find the mean and mode of the frequency distribution of daily wages of workers shown in the given table.
Step-by-Step Solution
Key Concept: Assumed mean / step-deviation method for mean. Modal class $160-180$ for mode.
Table setup with class marks $x_i$, $f_i$, step-deviations $u_i$. Total $\sum f_i = 110$, $\sum f_i u_i = 1$. [2.0 Marks]
$\text{Mean} = A + h \left(\dfrac{\sum f_i u_i}{\sum f_i}\right) = 170 + 20\left(\dfrac{1}{110}\right) = 170.18$. [1.5 Marks]
Modal class $160-180$. $l = 160, f_1 = 22, f_0 = 20, f_2 = 18, h = 20$.
$\text{Mode} = 160 + \left(\dfrac{22 - 20}{44 - 20 - 18}\right) \times 20 = 160 + \dfrac{40}{6} = 166.67$. [1.5 Marks]
$\text{Mean} = A + h \left(\dfrac{\sum f_i u_i}{\sum f_i}\right) = 170 + 20\left(\dfrac{1}{110}\right) = 170.18$. [1.5 Marks]
Modal class $160-180$. $l = 160, f_1 = 22, f_0 = 20, f_2 = 18, h = 20$.
$\text{Mode} = 160 + \left(\dfrac{22 - 20}{44 - 20 - 18}\right) \times 20 = 160 + \dfrac{40}{6} = 166.67$. [1.5 Marks]
Correct Answer: Mean $= ₹170.18$, Mode $= ₹166.67$
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