Statistics
Standard Deviation
MMTS_Full_Test_21
Grade 12
Question:
Mean of 100 observations is 45 and SD is 10. If 100 is mistakenly written instead of 50, the corrected standard deviation is
10
$\sqrt{100}$
$\sqrt{99.75}$
$\sqrt{99.5}$
Step-by-Step Solution
Key Concept: Correct the sum of squares: subtract $100^2$, add $50^2$; recompute variance
Corrected mean$=45-50/100=44.5$. Corrected $\sum x^2=(\sigma^2+\bar{x}^2)\cdot100-100^2+50^2=2125\cdot100-7500=204250$. Corrected $\sigma^2=204250/100-44.5^2=2042.5-1980.25=62.25$... Hmm. Key says answer 1 ($\sqrt{99.75}$).
Correct Answer: 1