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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Statistics

NTA Abhyas 2020 · Mathematics · Statistics

The mean of 40 observations is 20 and their standard deviation is 5...

The mean of 4040 observations is 2020 and their standard deviation is 5.5 . If the sum of the squares of the observations is kk, then the value of k1000\dfrac{k}{1000} is

Correct answer

17

Step-by-step solution

n=40n = 40
x¯=20\overset{¯}{x} = 20
σ=05\sigma = 05
σ2=∑xi240−(x¯)2{\sigma}^{2} = \dfrac{∑ {x}_{i}^{2}}{40} - {\left(\overset{¯}{x}\right)}^{2}
25=∑xi240−400⇒∑xi2=1700025 = \dfrac{∑ {x}_{i}^{2}}{40} - 400 ⇒ ∑ {x}_{i}^{2} = 17000
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