Question

Calculate Median salary from the following frequency distribution:

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

• A. $38.5$
• B. $36.98$
• C. $38.33$
• D. $39.00$

Answer 1

The correct option is C $38.33$

Median is the middle most value of a given series that represents the whole class of the series. For a group data,

Median = L + [{(n/2) – B}/G] × w where

• Lis the lower class boundary of the group containing the median
  
• nis the total number of values
  
• Bis the cumulative frequency of the groups before the median group
  
• Gis the frequency of the median group
  
• wis the group width
  

Since the median is the middle value, which in this case is the 10^th one, which is in the 30-40 group. Therefore , 30-40 is the median group so

• L= 30
  
• n= 20
  
• B= 2 + 3 = 5
  
• G= 6
  
• w= 10
  

Median= 30 + [{(20/2) – 5}/6] × 10

• = 30 + 8.33
  
• = 38.33