Find the mean of the following frequency distribution using assumed mean method:
Class: 10-25, 25-40, 40-55, 55-70, 70-85, 85-100
Frequency: 2, 3, 7, 6, 6, 6
Step-by-Step Solution
Key Concept: $x_i$: 17.5, 32.5, 47.5, 62.5, 77.5, 92.5. Let $a = 62.5$.<br>$d_i = x_i - 62.5$: -45, -30, -15, 0, 15, 30.<br>$f_i d_i$: -90, -90, -105, 0, 90, 180. $\sum f_i d_i = -15$.<br>$\sum f_i = 30$. $\bar{x} = 62.5 + (-15/30) = 62.5 - 0.5 = 62.0$.
Class marks $x_i = [17.5, 32.5, 47.5, 62.5, 77.5, 92.5]$. Let $a = 62.5$. [1.0 Mark]
$d_i = [-45, -30, -15, 0, 15, 30] \Rightarrow \sum f_i d_i = -15$. $\sum f_i = 30$. [1.0 Mark]
$\bar{x} = 62.5 - 0.5 = 62.0$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Finding class marks & assumed mean $a = 62.5$: 1.0 Mark
Calculating $\sum f_i d_i = -15$: 1.0 Mark
Evaluating mean $= 62.0$: 1.0 Mark
Correct Answer: