If each observation of the data is increased by 5, then their mean ______. - Mathematics

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If each observation of the data is increased by 5, then their mean ______.

Options

  • Remains the same

  • Becomes 5 times the original mean

  • Is decreased by 5

  • Is increased by 5

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Solution

If each observation of the data is increased by 5, then their mean is increased by 5.

Explanation:

Let x1, x2, .... xn be the n observations.

Then, old mean `barx_("old") = (sum_(i = 1)^n  x_i)/n`  ......(i)

Now, adding 5 in each observation, the new mean becomes

`barx_("new") = ((x_1 + 5) + (x_2 + 5) + ... + (x_n + 5))/n`

⇒ `barx_("new") = ((x_1 + x_2 + ... + x_n) + 5n)/n`

⇒ `barx_("new") = (sum_(i = 1)^n  x_i)/n + 5 = barx_("old") + 5`  .....[From equation (i)]

⇒ `barx_("new") = barx_("old") + 5`

Hence, the new mean is increased by 5.

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Chapter 14: Statistics & Probability - Exercise 14.1 [Page 133]

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NCERT Exemplar Mathematics Class 9
Chapter 14 Statistics & Probability
Exercise 14.1 | Q 14 | Page 133

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