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Let a, b, c, d, e be the observations with mean m and standard deviation s. The standard deviation of the observations a + k, b + k, c + k, d + k, e + k is ______. - Mathematics

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प्रश्न

Let a, b, c, d, e be the observations with mean m and standard deviation s. The standard deviation of the observations a + k, b + k, c + k, d + k, e + k is ______.

विकल्प

  • s

  • ks

  • s + k

  • `s/k`

MCQ
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उत्तर

Let a, b, c, d, e be the observations with mean m and standard deviation s. The standard deviation of the observations a + k, b + k, c + k, d + k, e + k is s.

Explanation:

Given observation are a, b, c, d and e

∴ Mean = m = `(a + b + c + d + e)/5`

∴ `sumx_i` = 5m

Now mean of a + k, b + k, c + k, d + k and e + k is

= `(a + k + b + k + c + k + d + k + e + k)/5`

= `((a + b + c + d + e) + 5k)/5`

= `(5m + 5k)/5`

= m + k

∴ S.D. = `sqrt((sum(x_i + k)^2)/n - [(sumx_i + k)/n]^2`

= `sqrt((sum(x_i^2 + k^2 + 2x_ik))/n - (m + k)^2`

= `sqrt((sumx_i^2)/n + (sumk^2)/n + (2ksumx_i)/n - m^2 - k^2 - 2mk)`

= `sqrt((sumx_i^2)/n + k^2 + 2km - m^2 - k^2 - 2mk)`

= `sqrt((sumx_i^2)/n - m^2)`  .....`[because (sumx_i)/n = m]`

= s

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अध्याय 15: Statistics - Exercise [पृष्ठ २८२]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
अध्याय 15 Statistics
Exercise | Q 31 | पृष्ठ २८२

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