Weight (in kg) 40 - 44 44 - 48 48 - 52 52 - 56 56 - 60 60 - 64 64 - 68 68 - 72
Number of students 4 6 10 14 10 8 6 2
The following distribution gives that weights of $60$ students of a class. Find the mean and mode weights of the students.

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Solution

Weight

Number of students

$x_{i}$

$f_{i} x_{i}$

40-44

4

42

168

44-48

6

46

276

48-52

10

50

500

52-56

14

54

756

56-60

10

58

580

60-64

8

62

496

64-68

6

66

396

68-72

2

70

140

$\sum f_{i} = 60$

$\sum f_{i} x_{i} = 3312$

$M e a n = \frac{\sum f_{i} x_{i}}{\sum f_{i}} = \frac{3312}{60} = 55.2 M o d e = l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h = 52 + (\frac{14 - 10}{28 - 10 - 10}) \times 4 = 52 + \frac{4}{8} \times 4 = 54 A n s .$

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60

Weight (in kg)	$40 - 44$	$44 - 48$	$48 - 52$	$52 - 56$	$56 - 60$	$60 - 64$	$64 - 68$	$68 - 72$
Number of students	$4$	$6$	$10$	$14$	$10$	$8$	$6$	$2$

52, 56, 72, 68, 52, 68, 52, 68, 52, 60, 56, 72, 56, 60, 64, 56, 48, 48, 64

64

Height (inches)	60	64	68	62	67	69	70	72	65	61
Weight (kg)	50	48	56	65	49	52	57	60	59	47

Marks of obtained by Mollie	44	80	76	48	52	72	68	56	60	54
Marks of obtained by Isha	48	75	54	60	63	69	72	51	57	66

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Weight (in kg)	40 - 44	44 - 48	48 - 52	52 - 56	56 - 60	60 - 64	64 - 68	68 - 72
Number of students	4	6	10	14	10	8	6	2