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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 x_{1}, x_{2}, .... x_{n} 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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