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Properties of Measures of Central Tendency

Question 11 C...

Question

Question 11
Consider the following distribution
$\begin{matrix} M a r k s o b t a i n e d & N u m b e r o f s t u d e n t s M o r e t h a n o r e q u a l t o 0 & 63 M o r e t h a n o r e q u a l t o 10 & 58 M o r e t h a n o r e q u a l t o 20 & 55 M o r e t h a n o r e q u a l t o 30 & 51 M o r e t h a n o r e q u a l t o 40 & 48 M o r e t h a n o r e q u a l t o 50 & 42 \end{matrix}$
the frequency of the class 30-40 is
(a) 3
(b) 4
(c) 48
(d) 51

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Solution

$\begin{matrix} M a r k s & N u m b e r o f s t u d e n t s 0 - 10 & (63 - 58) = 5 10 - 20 & (58 - 55) = 3 20 - 30 & (55 - 51) = 4 30 - 40 & (51 - 48) = 3 40 - 50 & (48 - 42) = 6 50 & 42 - 42 \end{matrix}$
Hence, frequency in the class interval 30-40 is 3.

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30 - 40

\begin{matrix} M a r k s (o u t o f 90) & N u m b e r o f s t u d e n t s M o r e t h a n o r e q u a l t o 80 & 4 M o r e t h a n o r e q u a l t o 70 & 6 M o r e t h a n o r e q u a l t o 60 & 11 M o r e t h a n o r e q u a l t o 50 & 17 M o r e t h a n o r e q u a l t o 40 & 23 M o r e t h a n o r e q u a l t o 30 & 27 M o r e t h a n o r e q u a l t o 20 & 30 M o r e t h a n o r e q u a l t o 10 & 32 M o r e t h a n o r e q u a l t o 0 & 34 \end{matrix}

\begin{matrix} M a r k s (o u t o f 90) & N u m b e r o f s t u d e n t s M o r e t h a n o r e q u a l t o 80 & 4 M o r e t h a n o r e q u a l t o 70 & 6 M o r e t h a n o r e q u a l t o 60 & 11 M o r e t h a n o r e q u a l t o 50 & 17 M o r e t h a n o r e q u a l t o 40 & 23 M o r e t h a n o r e q u a l t o 30 & 27 M o r e t h a n o r e q u a l t o 20 & 30 M o r e t h a n o r e q u a l t o 10 & 32 M o r e t h a n o r e q u a l t o 0 & 34 \end{matrix}

Profit (in lakhs in Rs)	Number of shops (frequency)
More than or equal to 5 More than or equal to 10 More than or equal to 15 More than or equal to 20 More than or equal to 25 More than or equal to 30 More than or equal to 35	30 28 16 14 10 7 3

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