Find the mean of the given data- Class interval Frequency fi Class mark xi di - xi -a ui - di-h- 0-100 40 50 -200 -2- 100-200 39 150 -100 -1- 200-300 34 250 0 0- 300-400 30 350 100 1- 400-500 45 450 200 2- -

Let A =250 [ Class interval amp; Frequency (f_i) amp; Class mark (x_i) amp; d_i = x_i A amp; u_i = d_i/h amp; f_i u_i; ...

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Standard X

Mathematics

Assumed Mean Method of Finding Mean

Find the mean...

Question

Find the mean of the given data:
$\begin{matrix} C l a s s i n t e r v a l & F r e q u e n c y (f_{i}) & C l a s s m a r k (x_{i}) & d_{i} = x_{i} - a & u_{i} = \frac{d_{i}}{h} 0 - 100 & 40 & 50 & - 200 & - 2 100 - 200 & 39 & 150 & - 100 & - 1 200 - 300 & 34 & 250 & 0 & 0 300 - 400 & 30 & 350 & 100 & 1 400 - 500 & 45 & 450 & 200 & 2 \end{matrix}$

0

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\frac{1}{188}

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250

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250.53

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Solution

The correct option is D $250.53$
Let A =250
$\begin{matrix} C l a s s i n t e r v a l & F r e q u e n c y (f_{i}) & C l a s s m a r k (x_{i}) & d_{i} = x_{i} - A & u_{i} = \frac{d_{i}}{h} & f_{i} u_{i} 0 - 100 & 40 & 50 & - 200 & - 2 & - 80 100 - 200 & 39 & 150 & - 100 & - 1 & - 39 200 - 300 & 34 & 250 & 0 & 0 & 0 300 - 400 & 30 & 350 & 100 & 1 & 30 400 - 500 & 45 & 450 & 200 & 2 & 90 T o t a l & \sum f_{i} = 188 & \sum f_{i} u_{i} = 1 \end{matrix}$
Mean $= A + \frac{\sum f_{i} u_{i}}{\sum f_{i}} \times h = 200 + (\frac{1}{188} \times 100)$
Mean = 250.53

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Find the mean of the given data: Class intervalFrequency(fi)Class mark(xi)di=xi−aui=dih0−1004050−200−2100−20039150−100−1200−3003425000300−400303501001400−500454502002

The correct option is D 250.53Let A =250 Class intervalFrequency(fi)Class mark(xi)di=xi−Aui=dihfiui0−1004050−200−2−80100−20039150−100−1−39200−30034250000300−40030350100130400−50045450200290Total∑fi=188∑fiui=1 Mean =A+∑fiui∑fi×h=200+(1188 ×100) Mean = 250.53