Calculate the mean of the following distribution using step - deviation method- Class Interval Frequency- 30 - 40 10- 40 - 50 6- 50 -60 8- 60-70 12- 70-80 5- 80 - 90 9- -

[ Class Interval amp;Frequency(f_i) amp;x_i amp;u_i=x_i a/h amp;f_iu_i; 30 40 amp;10 amp;35 ...

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Byju's Answer

Standard IX

Mathematics

Mean of Grouped Frequency Distribution by Assumed Mean Method

Calculate the...

Question

Calculate the mean of the following distribution using step - deviation method.

$\begin{matrix} Class Interval & Frequency 30 - 40 & 10 40 - 50 & 6 50 - 60 & 8 60 - 70 & 12 70 - 80 & 5 80 - 90 & 9 \end{matrix}$

59.6

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58.6

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Solution

The correct option is A 59.6
$\begin{matrix} Class Interval & Frequency (f_{i}) & x_{i} & u_{i} = \frac{x_{i} - a}{h} & f_{i} u_{i} 30 - 40 & 10 & 35 & - 3 & - 30 40 - 50 & 6 & 45 & - 2 & - 12 50 - 60 & 8 & 55 & - 1 & - 8 60 - 70 & 12 & 65 = a & 0 & 0 70 - 80 & 5 & 75 & 1 & 5 80 - 90 & 9 & 85 & 2 & 18 \sum f_{i} = 50 & \sum f_{i} u_{i} = - 27 \end{matrix}$

$∴ Mean = a + h \frac{\sum f_{i} u_{i}}{\sum f}$
$= 65 + 10 \times \frac{(- 27)}{50} = 65 - 5.4 = 59.6$

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Calculate the mean of the following distribution using step - deviation method. Class IntervalFrequency30−401040−50650−60860−701270−80580−909

The correct option is A 59.6Class IntervalFrequency(fi)xiui=xi−ahfiui30−401035−3−3040−50645−2−1250−60855−1−860−701265=a0070−805751580−90985218 ∑fi=50 ∑fiui=−27 ∴Mean=a+h∑fiui∑f =65+10×(−27)50=65−5.4=59.6

Calculate the mean of the following distribution using step - deviation method.

$\begin{matrix} Class Interval & Frequency 30 - 40 & 10 40 - 50 & 6 50 - 60 & 8 60 - 70 & 12 70 - 80 & 5 80 - 90 & 9 \end{matrix}$