हिंदी

Consider the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. If 1 is added to each number, the variance of the numbers so obtained is ______. - Mathematics

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प्रश्न

Consider the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. If 1 is added to each number, the variance of the numbers so obtained is ______.

विकल्प

  • 6.5

  • 2.87

  • 3.87

  • 8.25

MCQ
रिक्त स्थान भरें

उत्तर

Consider the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. If 1 is added to each number, the variance of the numbers so obtained is 8.25.

Explanation:

Given numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Numbers obtained when 1 is added to the above numbers is 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11.

∴ `sumx_i` = 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11

= `10/2 [2 xx 2 + (10 - 1) - 1]`

= `5[4 + 9]`

= `5 xx 13`

= 65

Now `sumx_i^2 = 2^2 + 3^2 + 4^2 + ... + 11^2`

= `(1^2 + 2^2 + 3^2 + 4^2 + ... + 11^2) - (1)^2`

= `(n(n + 1)(2n + 1))/6 - 1`

= `(11 xx 12 xx 23)/6 - 1`

= `22 xx 23 - 1`

= 506 – 1

= 505

∴ Variance `(sigma^2) = (dumx_i^2)/N - ((sumx_i)/N)^2`

= `505/10 - (65/10)^2`

= `50.5 - (6.5)^2`

= 50.5 – 42.25

= 8.25

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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 35 | पृष्ठ २८२

वीडियो ट्यूटोरियलVIEW ALL [1]

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