Question

Find the mean of the following frequency distribution: Class interval 12.5 - 17.5 17.5 -22.5 225-27.5 27.5-32.5 32,507.5 Frequency 2 22 19 14 3​

Answer 1

Question:

Find the mean of the following frequency distribution:

$\displaystyle{\begin{array}{|c|c|}\cline{1-2}\bf\:Class\:interval & \bf\:Frequency\\\cline{1-2}\sf\:12.5\:-\:17.5 & \sf\:2\\\cline{1-2}\sf\:17.5\:-\:22.5 & \sf\:22\\\cline{1-2}\sf\:22.5\:-\:27.5 & \sf\:19\\\cline{1-2}\sf\:27.5\:-\:32.5 & \sf\:14\\\cline{1-2}\sf\:32.5\:-\:37.5 & \sf\:3\\\cline{1-2}\end{array}}$

Answer:

The mean of the given frequency distribution is 24.5 units.

Step-by-step-explanation:

We have given a frequency distribution.

We have to find the mean of the distribution.

Now,

$\displaystyle{\begin{array}{|c|c|c|c|}\cline{1-4}\bf\:Class\:interval & \bf\:Class\:mark\:(\:x_i\:) & \bf\:Frequency\:(\:f_i\:) & \bf\:x_i\:f_i\\\cline{1-4}\sf\:12.5\:-\:17.5 & \sf\:15 & \sf\:2 & \sf\:30\\\cline{1-4}\sf\:17.5\:-\:22.5 & \sf\:20 & \sf\:22 & \sf\:440\\\cline{1-4}\sf\:22.5\:-\:27.5 & \sf\:25 & \sf\:19 & \sf\:475\\\cline{1-4}\sf\:27.5\:-\:32.5 & \sf\:30 & \sf\:14 & \sf\:420\\\cline{1-4}\sf\:32.5\:-\:37.5 & \sf\:35 & \sf\:3 & \sf\:105\\\cline{1-4} & & \sf\:\sum\:f_i\:=\:N\:=\:60 & \sf\:\sum\:x_i\:f_i\:=\:1470\\\cline{1-4}\end{array}}$

Now, we know that,

$\displaystyle{\pink{\sf\:Mean\:\overline{X}\:=\:\dfrac{\sum\:x_i\:f_i}{\sum\:f_i}}\sf\:\:\:-\:-\:-\:[\:Formula\:]}$

$\displaystyle{\implies\sf\:Mean\:\overline{X}\:=\:\dfrac{147\cancel{0}}{6\cancel{0}}}$

$\displaystyle{\implies\sf\:Mean\:\overline{X}\:=\:\cancel{\dfrac{147}{6}}}$

$\displaystyle{\implies\sf\:Mean\:\overline{X}\:=\:\cancel{\dfrac{73.5}{3}}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:Mean\:\overline{X}\:=\:24.5\:units}}}}$

∴ The mean of the given frequency distribution is 24.5 units.

Answer 2

Answer:

The mean of the given frequency distribution is 24.5 units.