Question

What is the value of mode for the following data:

Class interval	Frequency
$350-369$	$15$
$370-389$	$27$
$390-409$	$31$
$410-429$	$19$
$430-449$	$13$
$450-469$	$6$

• A. $390$
• B. $394.50$
• C. $394$
• D. $400$

Answer 1

The correct option is B $394.50$

Class interval	Frequency
349.5−369.5	15
369.5−389.5	27
389.5−409.5	31
409.5−429.5	19
429.5−449.5	13
449.5−469.5	6

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

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

where

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

Therefore, in the given sum the modal class is 389.5−409.5 so

• L = 389.5
  
• fm-1= 27
  
• fm= 31
  
• fm+1= 19
  
• w = 20
  

Mode = 389.5 + [(31 – 27)/{(31 − 27) + (31 − 19)}] × 20

= 389.5 + 5

= 394.50