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Measures of Central Tendency for Grouped Data

Heights of st...

Question

Heights of students of Class X are given in the following frequency distribution :
$\begin{matrix} Marks & 150 - 155 & 155 - 160 & 160 - 165 & 165 - 170 & 170 - 175 Number of students & 15 & 8 & 20 & 12 & 5 \end{matrix}$
Find the modal height.
Also, find the mean height. Compare and interpret the two measures of central tendency.

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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

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

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Heights of students of Class X are given in the foloowing frequency distribution:

Height (in cm)	150−155	155−160	160−165	165−170	170−175
Number of students	15	8	20	12	5

Find the modal height.
Also, find the mean height. Compare and interpret the two measures of central tendency. [CBSE 2014]

Q. Find the unknown entries a, b, c, d, e and f in the following distribution of heights of students in a class

\begin{matrix} H e i g h t (i n c m) & F r e q u e n c y & C u m u l a t i v e f r e q u e n c y 150 - 155 & 12 & a 155 - 160 & b & 25 160 - 165 & 10 & c 165 - 170 & d & 43 170 - 175 & e & 48 175 - 180 & 2 & f T o t a l & 50 \end{matrix}

Q. Consider the frequency distribution of the heights of 60 students of a class

Height (in cm)	No. of Students	Cumulative Frequency
150-155	16	16
155-160	12	28
160-165	9	37
165-170	7	44
170-175	10	54
175-180	6	60

The sum of the lower limit of the modal class and the upper limit of the median class is
(a) 310
(b) 315
(c) 320
(d) 330

Q. Question 12
Find the unknown entries a, b, c, d, e and f in the following distribution of heights of students in a class

\begin{matrix} H e i g h t (i n c m) & F r e q u e n c y & C u m u l a t i v e f r e q u e n c y 150 - 155 & 12 & a 155 - 160 & b & 25 160 - 165 & 10 & c 165 - 170 & d & 43 170 - 175 & e & 48 175 - 180 & 2 & f T o t a l & 50 \end{matrix}

Q. Consider the frequency distribution of the height of clan:-
Find median class

Height $c m$	$150 - 155$	$155 - 160$	$160 - 165$	$165 - 170$	$170 - 175$	$175 - 180$
No of student	$16$	$12$	$9$	$7$	$10$	$6$
Cummulative frequency	$16$	$28$	$37$	$44$	$54$	$60$

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Measures of Central Tendency for Grouped Data

Standard X Mathematics

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