Statistics
NCERT Exemplar Ch 12
CBSE_NCERT_EXEMPLAR_CH12
Grade 10
Question:
The mean of the following frequency distribution is $25$. Find the value of $p$.
Class: 0-10, 10-20, 20-30, 30-40, 40-50
Frequency: 5, 18, 15, p, 6
Step-by-Step Solution
Key Concept: Class marks $x_i$: 5, 15, 25, 35, 45. Equate $\bar{x} = \dfrac{\sum f_i x_i}{\sum f_i} = 25$.
Stepwise Solution:
$\sum f_i = 5 + 18 + 15 + p + 6 = 44 + p$. [0.5 Mark]
$\sum f_i x_i = (5 \times 5) + (18 \times 15) + (15 \times 25) + (p \times 35) + (6 \times 45) = 25 + 270 + 375 + 35p + 270 = 940 + 35p$. [1.0 Mark]
\dfrac{940 + 35p}{44 + p} = 25 \Rightarrow 940 + 35p = 1100 + 25p \Rightarrow 10p = 160 \Rightarrow p = 16. [1.5 Marks]
Marking Scheme:
• Finding $\sum f_i = 44+p$ and $\sum f_i x_i = 940+35p$: 1.5 Marks
• Solving equation $10p = 160 \Rightarrow p = 16$: 1.5 Marks
Correct Answer:
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