The monthly income of 100 families are given as below:
$\begin{matrix} Income in (in Rs) & Number of families 0 - 5000 & 8 5000 - 10000 & 26 10000 - 15000 & 41 15000 - 20000 & 16 20000 - 25000 & 3 25000 - 30000 & 3 30000 - 35000 & 2 35000 - 40000 & 1 \end{matrix}$
Calculate the modal income.

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Solution

As the class 10000 – 15000 has maximum frequency, so it is the modal class:

Therefore, l=10000, h=5000,
f=41
and $f_{1}$ =26
and $f_{2}$ =16

$M o d e = l + \frac{f - f_{1}}{2 f - f_{1} - f_{2}} \times h$

$= 10000 + \frac{41 - 26}{2 (41) - 26 - 16} \times 5000$

$= 10000 + 1875 = 11875$

Hence, mode = Rs.11875

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Similar questions

Q. Calculate the mode from the following data:

Monthly salary (in Rs)	No. of employees
0-5000	90
5000-1000	150
10000-15000	100
15000-20000	80
20000-25000	70
25000-30000	10

Look at the cumulative frequency distribution table given below:

$\begin{matrix} M o n t h l y i n c o m e & N u m b e r o f f a m i l i e s M o r e t h a n R s .10000 & 100 M o r e t h a n R s .14000 & 85 M o r e t h a n R s .18000 & 69 M o r e t h a n R s .20000 & 50 M o r e t h a n R s .25000 & 37 M o r e t h a n R s .30000 & 15 \end{matrix}$

Number of families having income range 20000 to 25000 is

(a) 19 (b) 16 (c) 13 (d) 22

Q. There are 5 members in a family. The monthly income of every member is given below. Find out the average income of family members.

\begin{matrix} 1st Member & ₹ 30,000 2nd Member & ₹ 40,000 3rd Member & ₹ 50,000 4th Member & ₹ 60,000 5th Member & ₹ 70,000 \end{matrix}

Q. Question 15
Weekly income of 600 families is tabulated below ?

\begin{matrix} W e e k l y i n c o m e (i n R s) & N u m b e r o f f a m i l i e s 0 - 1000 & 250 1000 - 2000 & 190 2000 - 3000 & 100 3000 - 4000 & 40 4000 - 5000 & 15 5000 - 6000 & 5 T o t a l & 600 \end{matrix}

Compute the median income.

Q. Complete the following Cumulative Frequency Table :

Class (Monthly income in Rs.)	Frequency (No. of individuals)	More than or equal to type cumulative frequency
1000-5000	45	...........
5000-10000	19	..........
10000-15000	16	..........
15000-20000	02	.........
20000-25000	05	.........
	Total N = 87

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The monthly income of 100 families are given as below: Income in (in Rs)Number of families0−500085000−100002610000−150004115000−200001620000−25000325000−30000330000−35000235000−400001 Calculate the modal income.

As the class 10000 – 15000 has maximum frequency, so it is the modal class: Therefore, l=10000, h=5000, f=41 and f1=26 and f2=16 Mode=l+f−f12f−f1−f2×h =10000+41−262(41)−26−16×5000 =10000+1875=11875 Hence, mode = Rs.11875

The monthly income of 100 families are given as below:
$\begin{matrix} Income in (in Rs) & Number of families 0 - 5000 & 8 5000 - 10000 & 26 10000 - 15000 & 41 15000 - 20000 & 16 20000 - 25000 & 3 25000 - 30000 & 3 30000 - 35000 & 2 35000 - 40000 & 1 \end{matrix}$
Calculate the modal income.