The arithmetic mean of the following frequency distribution is \(53\). Find the value of k.
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The arithmetic mean of the following frequency distribution is \(53\). Find the value of k.
Answer
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
\(\Rightarrow 53=50+\dfrac{(-260+20k)}{72+k}\)
\(\Rightarrow 3=+\dfrac{(-260+20k)}{72+k}\)
\(⇒ 3(72 + k) = -260 + 20k\)
\(⇒ 216 + 3k = -260 + 20k\)
\(⇒ 476 = 17k\)
\(⇒ k = 28\)
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