Question

calculate the mean median from the following data and find out mode using relation among mean,median and mode. Class; 0-10 10-20 20-30 30-40 40-50 50-60 60-70 Frequency; 10 20 30 40 50 60 70

Answer 1

1.Mean

We create a table by adding the columns to given data. The first column is for midpoint of class, $x_i$

and other column for product of frequency and midpoint of class $f_ix_i$

as shown below.

$\bar x=\frac{∑f_ix_i}{∑f_i}$

$\bar x=\frac{25+150+450+1050+900+660+325}{5+10+18+30+20+12+5}\\\bar x=35.6$

b)Median

We create a table by adding the columns to given data. First column is for cumulative frequency which is sum of frequencies up to that class interval as follows;

$median=L+(\frac{{\frac{N}{2}}−f_0}{f})h$

$median=30+(\frac{{\frac{100}{2}}−33}{30})10$

$=35.67$

c.(mode)

$Mode=L+(\frac{f_1−f_0}{2f_1−f_0−f_2})h$

$Mode=30+(\frac{30−18}{2×30−18−20})×10$

$=35.45$