Question 15 Weekly income of 600 families is tabulated below -WlineWeekly income - in - Rs - Number of familiesll Wline0-1000 - 250 11000-2000 - 190 2000-3000 - 100 13000-4000 - 40 14000-5000 - 15 15000-6000 - 511WlineTotal - 600 1Wline array Compute the median income-

First we construct a cumulative frequency table. [ nbsp; Weekly income (in Rs) amp; Number of families (f_i) amp; Cumulative frequency(c_f); ...

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Standard X

Mathematics

Finding Median of Grouped Data When Class Intervals Are Not Given

Question 15 W...

Question

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.

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Solution

First we construct a cumulative frequency table.
$\begin{matrix} W e e k l y i n c o m e (i n R s) & N u m b e r o f f a m i l i e s (f_{i}) & C u m u l a t i v e f r e q u e n c y (c_{f}) 0 - 1000 & 250 & 250 1000 - 2000 & 190 & 250 + 190 = 440 2000 - 3000 & 100 & 440 + 100 = 540 3000 - 4000 & 40 & 540 + 40 = 580 4000 - 5000 & 15 & 580 + 15 = 595 5000 - 6000 & 5 & 595 + 5 = 600 \end{matrix}$
It is given that, n = 600
$∴ \frac{n}{2} = \frac{600}{2} = 300$
The cumulative frequency greater than 300=440 that lies in the interval 1000-2000.
so median class=1000-2000
Here, (lower limit) $l = 1000$
$f (f r e q u e n c y o f m e d i a n c l a s s) = 190 c_{f} (c u m u l a t i v e f r e q u e n c y o f c l a s s p r e c e d i n g m e d i a n c l a s s) = 250 (c l a s s w i d t h) h = 1000 a n d (t o t a l o b s e r v a t i o n) n = 600 ∴ M e d i a n = l + (\frac{{\frac{n}{2} - c_{f}}}{f} \times h) = 1000 + \frac{(300 - 250)}{190} \times 1000 = 1000 + \frac{50}{190} \times 1000 = 1000 + \frac{5000}{19} = 1000 + 263.15 = 1263.15$
Hence, the median income Rs 1263.15.

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Similar questions

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. Weekly income of

600

families is given below. Find the median.

Income in $R s$ .	$0 - 1000$	$1000 - 2000$	$2000 - 3000$	$3000 - 4000$	$4000 - 5000$	$5000 - 6000$
Frequency	$250$	$190$	$100$	$40$	$15$	$5$

Q. Question 17
The monthly income of 100 families are given as below ?

\begin{matrix} 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 - 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.

Assumethere are four families in a country. The average per capita incomeof these families is Rs 5000. If the income of three families is Rs4000, Rs 7000 and Rs 3000 respectively, what is the income of thefourth family?

(i)Rs7500

(ii)Rs3000

(iii)Rs2000

(iv)Rs6000

The table below shows the number of employees of an office, classified according to the income-tax paid by them.

Income Tax

(Rupees)

Number of Employees

1000 − 2000

2000 − 3000

3000 − 4000

4000 − 5000

5000 − 6000

6000 − 7000

7000 − 8000

8000 − 9000

Compute the median income-tax.

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Question 15 Weekly income of 600 families is tabulated below ? Weekly income (in Rs)Number of families0−10002501000−20001902000−30001003000−4000404000−5000155000−60005Total600 Compute the median income.