Statistics
NCERT Exemplar Ch 12
CBSE_NCERT_EXEMPLAR_CH12
Grade 10
Question:
If the mean of the observations $x, x+3, x+5, x+7,$ and $x+10$ is $9$, then the mean of the last three observations is:
$10.33$
$11.33$
$11$
$9$
Step-by-Step Solution
Key Concept: Sum of 5 observations $= 5x + 25 = 45 \Rightarrow 5x = 20 \Rightarrow x = 4$. Last three observations: $9, 11, 14$.
Stepwise Solution:
Mean $= \dfrac{5x + 25}{5} = x + 5 = 9 \Rightarrow x = 4$. [0.5 Mark]
Last three observations are $x+5=9, x+7=11, x+10=14$.
Mean of last three $= \dfrac{9 + 11 + 14}{3} = \dfrac{34}{3} = 11.33$. [0.5 Mark]
Marking Scheme:
• Finding $x = 4$: 0.5 Mark
• Calculating mean of last three observations $= 34/3 = 11.33$: 0.5 Mark
Correct Answer: $11.33$
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