Find the mean of the following data- using assumed-mean method- - Class 0-20 20-40 40-60 60-80 80-100 100-120- Frequency 20 35 52 44 38 31- -

Solution: Class Frequency (fi) Mid values (xi) Deviation (di) di = (xi 50) (fidi) 0 20 20 10 40 800 ...

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Standard X

Mathematics

Assumed Mean Method of Finding Mean

Find the mean...

Question

Find the mean of the following data, using assumed-mean method:
$\begin{matrix} Class & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 & 100 - 120 Frequency & 20 & 35 & 52 & 44 & 38 & 31 \end{matrix}$

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Solution

Solution:
$\begin{matrix} Class & Frequency (f_{i}) & Mid values (x_{i}) & Deviation (d_{i} = x_{i} - 50) & f_{i} d_{i} 0 - 20 & 20 & 10 & - 40 & - 800 20 - 40 & 35 & 30 & - 20 & - 700 40 - 60 & 52 & 50 = A & 0 & 0 60 - 80 & 44 & 70 & 20 & 880 80 - 100 & 38 & 90 & 40 & 1520 100 - 120 & 31 & 110 & 60 & 1860 \sum f_{i} = 220 & \sum f_{i} d_{i} = 2760 \end{matrix}$
Let A= assumed mean = $50$ .
Mean, $¯ ¯ ¯ x = A + \frac{\sum f_{i} d_{i}}{\sum f_{i}}$
$= 50 + \frac{2760}{220}$
$= 50 + 12.55$
$= 62.55$

Hence, the mean of the given data is $62.55$

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Find the mean of the following data, using assumed-mean method: Class0−2020−4040−6060−8080−100100−120Frequency203552443831

Find the mean of the following data, using assumed-mean method:
$\begin{matrix} Class & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 & 100 - 120 Frequency & 20 & 35 & 52 & 44 & 38 & 31 \end{matrix}$