Find the mode- median and mean for the following data- Marks obtained 25-35 35-45 45-55 55-65 65-75 75-85- Number of- students 7 31 33 17 11 1- -

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

Find the mode...

Question

Find the mode, median and mean for the following data: $\begin{matrix} Marks obtained & 25 - 35 & 35 - 45 & 45 - 55 & 55 - 65 & 65 - 75 & 75 - 85 Number of students & 7 & 31 & 33 & 17 & 11 & 1 \end{matrix}$

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Solution

Marks obtained Frequency c.f

25-35 30 7 -30 7 -210

35-45 40 31 -20 38 -620

45-55 50 33 -10 71 -330

55-65 60 17 0 88 0

65-75 70 11 10 99 110

75-85 80 1 20 100 20

=-1030

Let A be 60

$M e a n equals a plus fraction numerator capital sigma f subscript i d subscript i over denominator capital sigma f subscript i end fraction equals 60 plus open parentheses fraction numerator negative 1030 over denominator 100 end fraction close parentheses space space space space space space space equals 60 minus 10.3 equals 49.7 M o d a l space c l a s s equals 45 minus 55 comma l equals 45 m o d e l equals l plus open parentheses fraction numerator 33 minus 31 over denominator 66 minus 48 end fraction close parentheses cross times 10 equals 45 plus 2 over 18 cross times 10 space space space space space space space space space equals 45 plus 1.1 equals 46.1 M e a n space equals 49.7 space M o d e equals 46.1 3 space M e d i a n equals M o d e plus 2 space M e a n M e d i a n equals fraction numerator 46.1 plus 99.4 over denominator 3 end fraction equals 48.5$

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Marks obtained		Frequency		c.f
25-35	30	7	-30	7	-210
35-45	40	31	-20	38	-620
45-55	50	33	-10	71	-330
55-65	60	17	0	88	0
65-75	70	11	10	99	110
75-85	80	1	20	100	20
					=-1030

Find the mode, median and mean for the following data:Marks obtained25−3535−4545−5555−6565−7575−85Number ofstudents7313317111

Marks obtained Frequency c.f 25-35 30 7 -30 7 -210 35-45 40 31 -20 38 -620 45-55 50 33 -10 71 -330 55-65 60 17 0 88 0 65-75 70 11 10 99 110 75-85 80 1 20 100 20 =-1030 Let A be 60

Find the mode, median and mean for the following data: $\begin{matrix} Marks obtained & 25 - 35 & 35 - 45 & 45 - 55 & 55 - 65 & 65 - 75 & 75 - 85 Number of students & 7 & 31 & 33 & 17 & 11 & 1 \end{matrix}$