Question

$\sf Find\:median \:of\:the\:Given\:Data$

$\boxed{\begin{array}{c|c|c|c|c|c|c}&&&&&&\\ \bf Class\:interval &\sf 0-10 &\sf 10-20 &\sf 20-30 &\sf 30-40 &\sf 40-50 &\sf 50-60 \\&&&&&&\\ \bf Frequency &\sf 5 &\sf 12 &\sf 22 &\sf 18 &\sf 10 &\sf 6 \end {array}}$

$\bf Note:-$

Draw a frequency table in your answer.

Spammed answers will be deleted.
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Answer 1

$\sf \therefore Mean=\dfrac{\Sigma fx}{\Sigma f}$

$\sf \to Mean=\dfrac{2165}{73}$

$\sf \to Mean=29\dfrac{48}{73}\:or\:29.65$

This is the direct method.

Step 1 → Find the mean (mid-value) of each class interval. The mean value of class interval is obtained by dividing the sum of its lower and upper limits by 2.

Step 2 → Represent the mean value by x and find the arithmetic mean using direct method.

There are two other methods to find the mean.

$\sf \underbrace{Short-Cut\:Method}$

In this method, an assumed mean (A) is taken according to the convenience and then the arithmetic mean is obtained by using the following formula:

$\sf Mean=A+\dfrac{\Sigma fd}{\Sigma f}$

Here, 'A' is the assumed mean and 'd' is the deviation of 'x' from assumed mean 'A'. Any number can be taken as assumed mean, but to make the calculations simpler, the assumed mean should be taken from the middle of the values of x.

$\sf \underbrace{Step-Deviation\:Method}$

According to this method;

$\sf Mean=A+\dfrac{\Sigma ft}{\Sigma f}\times i$

Here, A = Assumed mean

t = $\sf \dfrac{x-A}{i}$

i = class-size (i.e upper class limit - lower class limit)

Answer 2

Answer:

\sf \therefore Mean=\dfrac{\Sigma fx}{\Sigma f}∴Mean=ΣfΣfx

\sf \to Mean=\dfrac{2165}{73}→Mean=732165

\sf \to Mean=29\dfrac{48}{73}\:or\:29.65→Mean=297348or29.65

This is the direct method.

Step 1 → Find the mean (mid-value) of each class interval. The mean value of class interval is obtained by dividing the sum of its lower and upper limits by 2.

Step 2 → Represent the mean value by x and find the arithmetic mean using direct method.

There are two other methods to find the mean.

\sf \underbrace{Short-Cut\:Method}Short−CutMethod

In this method, an assumed mean (A) is taken according to the convenience and then the arithmetic mean is obtained by using the following formula:

\sf Mean=A+\dfrac{\Sigma fd}{\Sigma f}Mean=A+ΣfΣfd

Here, 'A' is the assumed mean and 'd' is the deviation of 'x' from assumed mean 'A'. Any number can be taken as assumed mean, but to make the calculations simpler, the assumed mean should be taken from the middle of the values of x.

\sf \underbrace{Step-Deviation\:Method}Step−DeviationMethod

According to this method;

\sf Mean=A+\dfrac{\Sigma ft}{\Sigma f}\times iMean=A+ΣfΣft×i

Here, A = Assumed mean

t = \sf \dfrac{x-A}{i}ix−A

i = class-size (i.e upper class limit - lower class limit)