Find the mean of the following distribution by Assumed Mean Method-Class interval - Frequency Whline10-20 - 8 Whline20-30 - 7 Whline30 -40-12 Whe40-50-23Whline50-60-11Mhline60-70-13Whline70-80 - 8 iWhline80-90 - 6 Whline90-100-12Whline end array

[ Class interval amp;Frequency (f_i) amp;X_i amp;d_i=X_i 55 amp;f_id_i; 10 20 amp; 8 amp; ...

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Byju's Answer

Standard X

Mathematics

Relation between Mean of Step- Deviations (U) and Mean

Find the mean...

Question

Find the mean of the following distribution by Assumed Mean Method:

$\begin{matrix} Class interval & Frequency 10 - 20 & 8 20 - 30 & 7 30 - 40 & 12 40 - 50 & 23 50 - 60 & 11 60 - 70 & 13 70 - 80 & 8 80 - 90 & 6 90 - 100 & 12 \end{matrix}$

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Solution

$\begin{matrix} Class interval & Frequency (f_{i}) & X_{i} & d_{i} = X_{i} - 55 & f_{i} d_{i} 10 - 20 & 8 & 15 & - 40 & - 320 20 - 30 & 7 & 25 & - 30 & - 210 30 - 40 & 12 & 35 & - 20 & - 240 40 - 50 & 23 & 45 & - 10 & - 230 50 - 60 & 11 & 55 & 0 & 0 60 - 70 & 13 & 65 & 10 & 130 70 - 80 & 8 & 75 & 20 & 160 80 - 90 & 6 & 85 & 30 & 180 90 - 10 & 12 & 95 & 40 & 480 \sum f_{i} = 100 & \sum f_{i} d_{i} = - 50 \end{matrix}$

Let A=55

Mean = $A + \frac{\sum f_{i} d_{i}}{\sum f_{i}} = 55 + (\frac{- 50}{100})$

$= 55 - \frac{- 50}{100} = 55 - 0.5 = 54.5$

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Find the mean of the following distribution by Assumed Mean Method: Class intervalFrequency10−20 820−30 730−401240−502350−601160−701370−80 880−90 690−10012

Find the mean of the following distribution by Assumed Mean Method:

$\begin{matrix} Class interval & Frequency 10 - 20 & 8 20 - 30 & 7 30 - 40 & 12 40 - 50 & 23 50 - 60 & 11 60 - 70 & 13 70 - 80 & 8 80 - 90 & 6 90 - 100 & 12 \end{matrix}$