Calculate - fiui- fi for the given data using step-deviation method- 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- -

[ nbsp; Class interval amp; Frequency (f_i) amp; Class mark (x_i) nbsp; amp; d_i = x_i a amp; u_i = d_i/h amp; f_i u_i; ...

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Byju's Answer

Standard X

Mathematics

Step Deviation Method

Calculate ∑ f...

Question

Calculate $\frac{\sum f_{i} u_{i}}{\sum f_{i}}$ for the given data using step-deviation method.
$\begin{matrix} Class interval & Frequency (f_{i}) & Class mark (x_{i}) & d_{i} = x_{i} - a & u_{i} = \frac{d_{i}}{h} 0 - 100 & 40 & 50 & - 200 & - 2 100 - 200 & 39 & 150 & - 100 & - 1 200 - 300 & 34 & 250 & 0 & 0 300 - 400 & 30 & 350 & 100 & 1 400 - 500 & 45 & 450 & 200 & 2 \end{matrix}$

\frac{1}{188}

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Solution

The correct option is A $\frac{1}{188}$
$\begin{matrix} Class interval & Frequency (f_{i}) & Class mark (x_{i}) & d_{i} = x_{i} - a & u_{i} = \frac{d_{i}}{h} & f_{i} u_{i} 0 - 100 & 40 & 50 & - 200 & - 2 & - 80 100 - 200 & 39 & 150 & - 100 & - 1 & - 39 200 - 300 & 34 & 250 & 0 & 0 & 0 300 - 400 & 30 & 350 & 100 & 1 & 30 400 - 500 & 45 & 450 & 200 & 2 & 90 Total & \sum f_{i} = 188 & \sum f_{i} u_{i} = 1 \end{matrix}$

$\frac{\sum f_{i} u_{i}}{\sum f_{i}} = \frac{1}{188}$

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Q. Calculate

\frac{\sum f_{i} u_{i}}{\sum f_{i}}

for the given data using step-deviation method.

\begin{matrix} Class interval & Frequency (f_{i}) & Class mark (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}

Find the mean of the step deviations:
$\begin{matrix} Class interval & Frequency (f_{i}) & Class mark (x_{i}) & d_{i} = x_{i} - a & u_{i} = \frac{d_{i}}{h} 0 - 100 & 40 & 50 & - 200 & - 2 100 - 200 & 39 & 150 & - 100 & - 1 200 - 300 & 34 & 250 & 0 & 0 300 - 400 & 30 & 350 & 100 & 1 400 - 500 & 45 & 450 & 200 & 2 \end{matrix}$

Q. 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}

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Calculate ∑fiui∑fi for the given data using step-deviation method. Class intervalFrequency(fi)Class mark(xi)di=xi−aui=dih0−1004050−200−2100−20039150−100−1200−3003425000300−400303501001400−500454502002

The correct option is A 1188Class intervalFrequency(fi)Class mark(xi)di=xi−aui=dihfiui0−1004050−200−2−80100−20039150−100−1−39200−30034250000300−40030350100130400−50045450200290Total∑fi=188∑fiui=1 ∑fiui∑fi=1188