wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Heights of students of Class X are given in the following frequency distribution :
Marks150155155160160165165170170175Number ofstudents15820125
Find the modal height.
Also, find the mean height. Compare and interpret the two measures of central tendency.

Open in App
Solution

Estimated mode is given by

m o d e space equals space L space plus space fraction numerator f subscript m minus f subscript m minus 1 end subscript over denominator open parentheses f subscript m minus f subscript m minus 1 end subscript close parentheses space plus space open parentheses f subscript m minus f subscript m plus 1 end subscript close parentheses end fraction cross times ww h e r e commaL space i s space t h e space l o w e r space c l a s s space b o u n d a r y space o f space t h e space m o d a l space g r o u p space space space space spacef subscript m minus 1 end subscript space i s space t h e space f r e q u e n c y space o f space t h e space g r o u p space b e f o r e space t h e space m o d a l space g r o u pf subscript m space i s space t h e space f r e q u e n c y space o f space t h e space m o d a l space g r o u p space space space space spacef subscript m plus 1 space end subscript i s space t h e space f r e q u e n c y space o f space t h e space g r o u p space a f t e r space t h e space m o d a l space g r o u p space space space spacew space i s space t h e space g r o u p space w i d t h

h e r e space t h e space m o d a l space c l a s s space i s space 160 minus 165 h e n c e L space equals space 160 f subscript m minus 1 end subscript space equals space 8 f subscript m space equals space 20 f subscript m plus 1 end subscript space equals space 12 w space equals 5 s o m o d e space equals space 160 space plus fraction numerator 20 minus 8 over denominator 20 minus 8 space plus space 20 minus 12 end fraction cross times 5 space equals space 160 space plus thin space 3 space equals space 163


for calculating mean
w e space n e e d space t o space f i n d space t h e space m i d p o i n t space o f space e a c h space c l a s s space i n t e r v a l s o m i d p o i n t s space a r e space c l a s s space i n t e r v a l space space space space space space space space m i d p o i n t left parenthesis f right parenthesis space space space space 150 minus 155 space space space space space space space space space space space space space 152.5 space space space space 155 minus 160 space space space space space space space space space space space space space 157.5 space space space space 160 minus 165 space space space space space space space space space space space space space 162.5 space space space space 165 minus 170 space space space space space space space space space space space space space 167.5 space space space space 170 minus 175 space space space space space space space space space space space space space 172.5 a n d space m u l t i p l y space t h e s e space m i d p o i n t s space w i t h space t h e space c o r r e s p o n d i n g space f r e q u e n c i e s space o f space t h e i r space c l a s s e s space a n d space a d d space a l l space o f space t h e m s o space 152.5 cross times 15 space plus space 157.5 cross times 8 space plus space 162.5 cross times 20 space plus space 167.5 cross times 12 space plus 172.5 space cross times 5 space equals space 9670 t o t a l space f r e q u e n c y space equals space 15 plus 8 plus 20 plus 12 plus 5 space equals space 60 h e n c e space m e a n space equals space 9670 over 60 space equals space 161.166

here the mean is less than mode and If the mean is less than the mode, the distribution is negatively skewed


flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Mode
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon