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# Question and Answer

The arithmetic mean of the following frequency distribution is $$53$$. Find the value of k.
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## QuestionMathsClass 10

The arithmetic mean of the following frequency distribution is $$53$$. Find the value of k.

Use the shortcut method to find the mean of given data.
For that,
Let the assumed mean be $$(A) = 2$$,
The deviation of values xi from assumed mean be di = xi $$– A$$.
Now to find the mean:
First multiply the frequencies in column (ii) with the value of deviations in column (iv) as fidi.
Now add the sum of all entries in column (iv) to obtain$$\sum_{i=1}^{n}f_id_i$$and the sum of all frequencies in the column (ii) to obtain
$$\sum_{i=1}^{n}f_i=N$$
So,
=$$Mean(\overline{x})=A+\dfrac{\sum f_id_i}{N}$$
where, N = total number of observations
$$\Rightarrow 53=50+\dfrac{(-260+20k)}{72+k}$$
$$\Rightarrow 3=+\dfrac{(-260+20k)}{72+k}$$
$$⇒ 3(72 + k) = -260 + 20k$$
$$⇒ 216 + 3k = -260 + 20k$$
$$⇒ 476 = 17k$$
$$⇒ k = 28$$