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Standard XI

Statistics

Mean Deviation from Mean for Continuous Series

Calculate the...

Question

Calculate the arithmetic mean of given frequency distribution table.
Class-interval $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$
Frequency $7$ $14$ $28$ $26$ $16$ $9$

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Solution

class interval frequency (f) mean value (x) $f x$
0 - 10 7 5 35
10 - 20 14 15 210
20 - 30 28 25 700
30 - 40 26 35 910
40 - 50 19 45 720
50 - 60 9 55 495
Sum 100 3070
$A . M . = \frac{\sum f_{i} x_{i}}{\sum f_{i}} = \frac{3070}{100} = 30.7$

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Q. Calculate the mean of the following distribution:

Class Interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
Frequency	$8$	$5$	$12$	$35$	$24$	$16$

Q. Find the mean for the following distribution table, using Deviation method.

Class Interval	$0 - 9$	$10 - 19$	$20 - 29$	$30 - 39$	$40 - 49$	$50 - 50$	$60 - 60$
Frequency	$8$	$10$	$22$	$26$	$18$	$9$	$7$

Q. The arithmetic mean of the following frequency distribution is 50.

Class	0-10	10-20	20-30	30-40	40-50
Frequency	16	p	30	32	14

Find the value of p.

Q. Find the mean deviation about the following continuous distribution:

Class interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$5$	$8$	$7$	$12$	$28$	$20$	$10$	$10$

Q. Calculate the mean of the following distribution: [4 MARKS]

\begin{matrix} C l a s s I n t e r v a l & F r e q u e n c y 0 - 10 & 8 10 - 20 & 5 20 - 30 & 12 30 - 40 & 35 40 - 50 & 24 50 - 60 & 16 \end{matrix}

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Calculate the arithmetic mean of given frequency distribution table.
Class-interval $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$
Frequency $7$ $14$ $28$ $26$ $16$ $9$

class interval frequency (f) mean value (x) $f x$
0 - 10 7 5 35
10 - 20 14 15 210
20 - 30 28 25 700
30 - 40 26 35 910
40 - 50 19 45 720
50 - 60 9 55 495
Sum 100 3070
$A . M . = \frac{\sum f_{i} x_{i}}{\sum f_{i}} = \frac{3070}{100} = 30.7$

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Class-interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
Frequency	$7$	$14$	$28$	$26$	$16$	$9$

class interval	frequency (f)	mean value (x)	$f x$
0 - 10	7	5	35
10 - 20	14	15	210
20 - 30	28	25	700
30 - 40	26	35	910
40 - 50	19	45	720
50 - 60	9	55	495
Sum	100		3070

Calculate the arithmetic mean of given frequency distribution table.Class-interval0−1010−2020−3030−4040−5050−60Frequency7142826169

class interval frequency (f) mean value (x) fx0 - 10 7 5 35 10 - 20 14 15 210 20 - 30 28 25 700 30 - 40 26 35 910 40 - 50 19 45 720 50 - 60 9 55 495 Sum 100 3070A.M.=∑fixi∑fi=3070100=30.7

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Calculate the arithmetic mean of given frequency distribution table.
Class-interval $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$
Frequency $7$ $14$ $28$ $26$ $16$ $9$

class interval frequency (f) mean value (x) $f x$
0 - 10 7 5 35
10 - 20 14 15 210
20 - 30 28 25 700
30 - 40 26 35 910
40 - 50 19 45 720
50 - 60 9 55 495
Sum 100 3070
$A . M . = \frac{\sum f_{i} x_{i}}{\sum f_{i}} = \frac{3070}{100} = 30.7$