Question

What is the value of median for the following data:

Marks	No. of Students
$5-14$	$10$
$15-24$	$18$
$25-34$	$32$
$35-44$	$26$
$45-54$	$14$
$55-64$	$10$

• A. $28$
• B. $30$
• C. $32.94$
• D. $33.18$

Answer 1

The correct option is C $32.94$

Marks	No. of Students
4.5 −14.5	10
14.5 −24.5	18
24.5 −34.5	32
34.5 −44.5	26
44.5−54.5	14
54.5−64.5	10

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 55th one, which is in the 24.5 −34.5 group. Therefore , 24.5 −34.5 is the median group so

• L= 24.5
  
• n= 110
  
• B= 10 +18 = 28
  
• G= 32
  
• w= 10
  

Median= 24.5 + [{(110/2) – 28}/32] × 10

• = 24.5 + 8.44
  
• = 32.94