Question

Calculate Mode salary from the following frequency distribution:

X in Rs. (000)	10-20	20-30	30-40	40-50	50-60	60-70
Y Frequency	2	3	6	5	2	2

• A. 37.5
• B. 37
• C. 38.5
• D. 39

Answer 1

The correct option is A 37.5

Mode is the value which occurs the highest number of times in a series.

Mode= L + [ (f_m − f_m-1)/{(f_m − f_m-1) + (f_m − f_m+1)}] × w

where

• L is the lower class boundary of the modal group
  
• f_m-1is the frequency of the group before the modal group
  
• f_mis the frequency of the modal group
  
• f_m+1is the frequency of the group after the modal group
  
• w is the group width
  

Therefore, in the given sum the modal class is 30-40 so

• L = 30
  
• f_m-1= 3
  
• f_m= 6
  
• f_m+1= 5
  
• w = 10
  

Mode = 30 + [(6 – 3)/{(6 − 3) + (6 − 5)}] × 10

= 30 + (3/4) × 10

= 37.5