Following information pertains to the daily income of 150 families- Calculate the arithmetic mean- - Income -in Rs- amp-Number of Families- More than 75 amp-150- More than 85 amp-140- More than 95 amp-115- More than 105 amp-95- More than 115 amp-70- More than 125 amp-60- More than 135 amp-40- More than 145 amp-25- -

[ Income Class amp;Number of Families amp;Frequency amp;Mid Value amp;fm; interval amp;( ...

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Standard XI

Statistics

Mean of Discrete Series

Following inf...

Question

Following information pertains to the daily income of 150 families. Calculate the arithmetic mean.

$\begin{matrix} Income (in Rs) & Number of Families More than 75 & 150 More than 85 & 140 More than 95 & 115 More than 105 & 95 More than 115 & 70 More than 125 & 60 More than 135 & 40 More than 145 & 25 \end{matrix}$

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Solution

$\begin{matrix} Income Class & Number of Families & Frequency & Mid Value & fm interval & (cf) & (f) & (m) 75 - 85 & 150 & 150 - 140 = 10 & 80 & 800 85 - 95 & 140 & 140 - 115 = 25 & 90 & 2250 95 - 105 & 115 & 115 - 95 = 20 & 100 & 2000 105 - 115 & 95 & 95 - 70 = 25 & 110 & 2750 115 - 125 & 70 & 70 - 60 = 10 & 120 & 1200 125 - 135 & 60 & 60 - 40 = 20 & 130 & 2600 135 - 145 & 40 & 40 - 25 = 15 & 140 & 2100 145 - 155 & 25 & 25 & 150 & 3750 Total & \sum f = 150 & \sum f m = 17, 450 \end{matrix}$

Mean $= \frac{\sum f m}{\sum f} = \frac{17, 450}{150} = R s 116.33$

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Similar questions

Q. Calculate arithemtic eman from the foolowing data:

Marks	No. Students
More than 0	150
More than 10	140
More than 20	100
More than 30	80
More than 40	80
More than 50	70
More than 60	30
More than 70	14

Q. In the following distribution :

Monthly income range (in Rs.)	Number of families
Income more than Rs. $10000$	$100$
Income more than Rs. $13000$	$85$
Income more than Rs. $16000$	$69$
Income more than Rs. $19000$	$50$
Income more than Rs. $22000$	$33$
Income more than Rs. $25000$	$15$

The numbers of families having income range (in Rs)

16000 - 19000

is:

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

Make a frequency table from the following:

Q. Compute the median for each of the following data:

(i)Marks	No. of students	(ii)Marks	No. of students
Less than $10$	$0$	More than $150$	$0$
Less than $30$	$10$	More than $140$	$12$
Less than $50$	$25$	More than $130$	$27$
Less than $70$	$43$	More than $120$	$60$
Less than $90$	$65$	More than $110$	$105$
Less than $110$	$87$	More than $100$	$124$
Less than $130$	$96$	More than $90$	$141$
Less than $150$	$100$	More than $80$	$150$

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Following information pertains to the daily income of 150 families. Calculate the arithmetic mean. Income (in Rs)Number of FamiliesMore than 75150More than 85140More than 95115More than 10595More than 11570More than 12560More than 13540More than 14525