Statistics
NCERT Exemplar Ch 12
CBSE_NCERT_EXEMPLAR_CH12
Grade 10
Question:
The mean of the following data is $14$. Find the value of $k$.
$x_i$: 5, 10, 15, 20, 25
$f_i$: 7, k, 8, 4, 5
Step-by-Step Solution
Key Concept: Mean $\bar{x} = \dfrac{\sum f_i x_i}{\sum f_i} = 14$.
Stepwise Solution:
$\sum f_i = 7 + k + 8 + 4 + 5 = 24 + k$. [0.5 Mark]
$\sum f_i x_i = (5 \times 7) + (10 \times k) + (15 \times 8) + (20 \times 4) + (25 \times 5) = 35 + 10k + 120 + 80 + 125 = 360 + 10k$. [0.5 Mark]
\dfrac{360 + 10k}{24 + k} = 14 \Rightarrow 360 + 10k = 336 + 14k \Rightarrow 4k = 24 \Rightarrow k = 6. [1.0 Mark]
Marking Scheme:
• Calculating $\sum f_i = 24+k$ and $\sum f_i x_i = 360+10k$: 1.0 Mark
• Solving for $k = 6$: 1.0 Mark
Correct Answer:
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