Question 9
Consider the data
$\begin{matrix} C l a s s & 65 - 85 & 85 - 105 & 105 - 125 & 125 - 145 & 145 - 165 & 165 - 185 & 185 - 205 F r e q u e n c y & 4 & 5 & 13 & 20 & 14 & 7 & 4 \end{matrix}$
The difference of the upper limit of the median class and the lower limit of the modal calss is
(a) 0
(b) 19
(c) 20
(d) 38

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Solution

$\begin{matrix} C l a s s & F r e q u e n c y & C u m u l a t i v e f r e q u e n c y 65 - 85 & 4 & 4 85 - 105 & 5 & 9 105 - 125 & 13 & 22 125 - 145 & 20 & 42 145 - 165 & 14 & 56 165 - 185 & 7 & 63 185 - 205 & 4 & 67 \end{matrix}$
Here, $\frac{N}{2} = \frac{67}{2} = 33.5$ which lies in the interval 125-145.
Hence, upper limit of median calss is 145.
Here, we see that the highest frequency is 20 which lies in 125-145. Hence, the lower limit of modal class is 125.
$∴$ Required difference =Upper limit of median class-Lower limit of modal class =145-125=20

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Similar questions

Consider the data

$\begin{matrix} Class & 65 - 85 & 85 - 105 & 105 - 125 & 125 - 145 & 145 - 165 & 165 - 185 & 185 - 205 Frequency & 4 & 5 & 13 & 20 & 14 & 7 & 4 \end{matrix}$

The difference of the upper limit of the median class and the lower limit of the modal calss is
(a) $0$
(b) $19$
(c) $20$
(d) $38$

Q. Consider the following frequency distributions:
Class: 65-85 85-105 105-125 125-145 145-165 165-185 - 185-205

Frequency: 4 5 13 20 14 7 4

The difference of the upper limit of the median class and the lower limit of the modal class is
(a) 0 (b) 19 (c) 20 (d) 38

Q. Question 6
For the following distribution,

\begin{matrix} C l a s s & 0 - 5 & 5 - 10 & 10 - 15 & 15 - 20 & 20 - 25 F r e q u e n c y & 10 & 15 & 12 & 20 & 9 \end{matrix}

the sum of lower limits of the median class and modal class is
(a) 15
(b) 25
(c) 30
(d) 35

Q. Identify the modal class, the upper limit of the modal class and the lower limit of the modal class for the given data:

\begin{matrix} A g e (i n y e a r s) & 5 - 15 & 15 - 25 & 25 - 35 & 35 - 45 & 45 - 55 & 55 - 65 N u m b e r o f p a t i e n t s & 6 & 11 & 21 & 23 & 14 & 5 \end{matrix}

Q. The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.

Monthly consumption: (in units)	65−85	85−105	105−125	125−145	145−165	165−185	185−205
No. of consumers:	4	5	13	20	14	8	4

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Class Interval

Standard X Mathematics

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Question 9 Consider the data Class65−8585−105105−125125−145145−165165−185185−205Frequency4513201474 The difference of the upper limit of the median class and the lower limit of the modal calss is (a) 0 (b) 19 (c) 20 (d) 38