Question

Find the mean, mode and median for the following data: Classes 0-10 10-20 20-30 30-40 40-50 50-60 60-70 Frequency 5 8 15 20 14 8 5

Answer 1

Answer:

Mean $=34.87,$ Mode $=34.55,$ Median $=34.75.$

Step-by-step explanation:

Let assumed mean $a=35,$ $h=$ lenghth of class interval $=10$

Mean,

    $=a+\frac{Sum of f_ix_i}{Sum of f_i} *h=35-\frac{1}{75} *10$

    $=35-\frac{2}{15}$

    $=35-0.13$

    $=34.87$

Since, Maximum frequency $=20$

Therefore, Model class $=30-40$

$l=30,f_1=20,f_0=15,f_2=14$

Mode,

         $=l+h\frac{f_1-f_0}{2f_1-f_0-f_2}$

         $=30+10(\frac{20-15}{40-50-14} )$

         $=30+\frac{50}{11}$

         $=30+4.55\\=34.55$

Hence, Mode is $34.55.$

Since, $\frac{N}{2} =\frac{75}{2} =37.5,$ which lies in the class $30-40$

Median class $=30-40$

$l_1=30,\frac{N}{2} =37.5, C=28, f=20,h=10$

Median is,

         $=l_1+\frac{\frac{N}{2} -C*h}{f}$

         $=30+\frac{37.5-28}{20} *10$

         $=30+\frac{9.5}{2}\\ =30+4.75\\=34.75$

Hence, Median is $34.75.$