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Best Suited Measure of Central Tendency in Different Cases and the Empirical Relationship between Them

Find the mean...

Question

Find the mean, median and mode of the following data:
$\begin{matrix} Class & 0 - 20 & 20 - 40 & 40 - 60 & 60 - 80 & 80 - 100 & 100 - 120 & 120 - 140 Frequency & 6 & 8 & 10 & 12 & 6 & 5 & 3 \end{matrix}$

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Solution

Classes Frequency Cumulative Frequency

0-20 6 6

20-40 8 14

40-60 10 24

60-80 12 36

80-100 6 42

100-120 5 47

120-140 3 50

$N equals 50 rightwards double arrow N over 2 equals 25 M e d i a n space c l a s s equals 60 minus 80 H e r e comma l equals 60 comma f equals 12 comma F equals 24 comma h equals 20 M e d i a n equals l plus open parentheses fraction numerator begin display style N over 2 end style minus F over denominator f end fraction close parentheses cross times h space space space space space space space space space space space equals 60 plus open parentheses fraction numerator 25 minus 24 over denominator 12 end fraction close parentheses cross times 20 space space space space space space space space space space space space equals 60 plus 1 over 12 cross times 20 equals 185 over 3 equals 61.6 M o d a l space c l a s s equals 60 minus 80 l equals 30 comma f equals 12 comma f subscript 1 equals 10 comma f subscript 2 equals 6 comma h equals 20 M o d e equals l plus fraction numerator f minus f subscript 1 over denominator 2 f minus f subscript 1 minus f subscript 2 end fraction cross times h space space space space space space space space space equals 60 plus fraction numerator 12 minus 10 over denominator 2 cross times 12 minus 10 minus 6 end fraction cross times 10 space space space space space space space space space space space equals 60 plus 2 over 8 cross times 20 equals 65 M o d e equals 3 space M e d i a n minus 2 space M e a n space 65 equals 3 cross times 61.6 minus 2 M e a n 2 space M e a n equals 184.8 minus 65 equals 119.8 M e a n equals fraction numerator 119.8 over denominator 2 end fraction equals 59.9 H e n c e space comma M e a n equals 59.9 space comma M o d e equals 65 comma M e d i a n equals 61.6$

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Q. Find the mean, median and mode of the following data:

Classes:	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	$100 - 120$	$120 - 140$
Frequency:	$6$	$8$	$10$	$12$	$6$	$5$	$3$

Q. Find the median of the following data:

Class interval	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	$100 - 120$	$120 - 140$
Frequency	$6$	$8$	$10$	$12$	$6$	$5$	$3$

Q. Find the mean of the following distribution.

Class	Frequency
$0 - 20$	$5$
$20 - 40$	$8$
$40 - 60$	$10$
$60 - 80$	$12$
$80 - 100$	$7$
$100 - 120$	$8$

Q. Find the mean, median and mode of the following data:

Classes:	0−20	20−40	40−60	60−80	80−100	100−120	120−140
Frequency:	6	8	10	12	6	5	3

Find the mean, mode and median of the following data: [CBSE 2008]

Class	0−20	20−40	40−60	60−80	80−100	100−120	120−140
Frequency	6	8	10	12	6	5	3

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Best Suited Measure of Central Tendency in Different Cases and the Empirical Relationship between Them

Standard X Mathematics

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