Calculate the mean, median and mode of the following frequency distribution:Classintervals:15 - 20 20 - 25 25 - 30 30 - Maths - Statistics

Question

Calculate the mean, median and mode of the following
frequency
distribution:Classintervals:15 - 20 20 - 25 25 - 30 30 - 35 35 - 40
40 45 45 - 50 50 55Frequency: 3 8 9 10 4 3 2 1Draw the less than
and more than O give (Cumulative Frequency Curve) for theabove data
and hence find the median

Manbar Singh · Accepted Answer

C
I

fi

xi

fi xi

15 - 20
3
17 5
87 5

20 - 25
8
22 5
180

25 - 30
9
27 5
247 5

30 - 35
10
32 5
325

35 - 40
4
37 5
150

40 - 45
3
42 5
127 5

45 - 50
2
47 5
95

50 - 55
1
52 5
52 5

Æ©fi =
40â€‹

Æ©fi xi
= 1265

Mean = ∑fi xi∑fi         = 126540         = 31
625

Now, Modal class = 30 - 35Lower limit of modal class = l = 30Frequency of modal class, f1 = 10Frequency of class preceeding modal class, f0 = 9Frequency of class succeeding modal class, f2 = 4Class size, h = 5Now, mode = l + f1 - f02f1 - f0 - f2 × h                             = 30 + 10 - 920 - 9 - 4 × 5                             = 30 + 17 × 5                             = 210 + 57                             = 2157                             = 30
71Median = Mode + 2 Mean3                      = 30
71 + 63
253                      = 93
963 = 31 32

C I	*f_i*	*x_i*	*f_ix_i*
15 - 20	3	17.5	87.5
20 - 25	8	22.5	180
25 - 30	9	27.5	247.5
30 - 35	10	32.5	325
35 - 40	4	37.5	150
40 - 45	3	42.5	127.5
45 - 50	2	47.5	95
50 - 55	1	52.5	52.5
	Ʃf_i = 40		Ʃf_i x_i = 1265

Calculate the mean, median and mode of the following frequencydistribution:Classintervals:15 - 20 20 - 25 25 - 30 30 - 35 35 - 40 40 45 45 - 50 50 55Frequency: 3 8 9 10 4 3 2 1Draw the less than and more than O give (Cumulative Frequency Curve) for theabove data and hence find the median.

Calculate the mean, median and mode of the following frequency
distribution:Classintervals:15 - 20 20 - 25 25 - 30 30 - 35 35 - 40 40 45 45 - 50 50 55Frequency: 3 8 9 10 4 3 2 1Draw the less than and more than O give (Cumulative Frequency Curve) for theabove data and hence find the median.