Question

Calculate the Median and Mode from the following data:
Annual Sales(Rs.000) Frequency
Less than 10 4
Less than 20 20
Less than 30 35
Less than 40 55
Less than 50 62
Less than 60 67

Answer 1

Solution

Median:

$$median= L+{h \over f}({N \over 2}-cf)$$

${N \over 2}= {67 \over 2}=33.5$ Therefore, 20-29 is the median class

$$19.5 +{10 \over 15}({67\over 2}-20)$$

= 28.5

=Rs. 28500

Mode:

$$mode = L+ {f_m - f_{m-1} \over 2f_m- f_{m-1}-f_{m+1}}$$

30-39 is the modal class since it has the highest frequency

$$\therefore mode = 29.5 + ({20-15 \over 2(20)-15-7})*10$$

=32.27778

=Rs. 32277.78