The following are the marks obtained by 70 boys in a class test.
Marks No. of boys
30 - 40 10
40 - 50 12
50 - 60 14
60 - 70 12
70 - 80 9
80 - 90 7
90 - 100 6
Calculate the mean by :
(i) Short-cut method
(ii) Step-deviation method
Measures of Central Tendency
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Question

The following are the marks obtained by 70 boys in a class test.
Marks No. of boys
30 - 40 10
40 - 50 12
50 - 60 14
60 - 70 12
70 - 80 9
80 - 90 7
90 - 100 6
Calculate the mean by :
(i) Short-cut method
(ii) Step-deviation method

Measures of Central Tendency

24 Likes

KnowledgeBoat · Accepted Answer

(i) Let assumed mean (A) be 65. Marks | Mid value (x) | No. of boys (f) | d = x - A | fd ---- | --- | --- | --- | ---- 30 - 40 | 35 | 10 | 35 - 65 = -30 | -300 40 - 50 | 45 | 12 | 45 - 65 = -20 | -240 50 - 60 | 55 | 14 | 55 - 65 = -10 | -140 60 - 70 | 65 | 12 | 65 - 65 = 0 | 0 70 - 80 | 75 | 9 | 75 - 65 = 10 | 90 80 - 90 | 85 | 7 | 85 - 65 = 20 | 140 90 - 100 | 95 | 6 | 95 - 65 = 30 | 180 Total | | Σf = 70 | | Σfx = -270 n = Σf = 70. By formula, Mean = A + = 65 - 3.86 = 61.14 Hence, mean = 61.14 (ii) We get mean values from part (i) and assumed mean (A) = 65. Let i = 10. Marks | Mid value (x) | No. of boys (f) | d = x - A | t = (x - A)/i | ft ---- | ---- | ----- | ----- | ----- | -------- 30 - 40 | 35 | 10 | 35 - 65 = -30 | -3 | -30 40 - 50 | 45 | 12 | 45 - 65 = -20 | -2 | -24 50 - 60 | 55 | 14 | 55 - 65 = -10 | -1 | -14 60 - 70 | 65 | 12 | 65 - 65 = 0 | 0 | 0 70 - 80 | 75 | 9 | 75 - 65 = 10 | 1 | 9 80 - 90 | 85 | 7 | 85 - 65 = 20 | 2 | 14 90 - 100 | 95 | 6 | 95 - 65 = 30 | 3 | 18 Total | | Σf = 70 | | | Σft = -27 n = Σf = 70. By formula, Mean = A + = 65 + = 65 - = 65 - 3.86 = 61.14 Hence, mean = 61.14

Age (years)	No. of students
16 - 18	2
18 - 20	7
20 - 22	21
22 - 24	17
24 - 26	3

C.I.	Frequency
63 - 70	9
70 - 77	13
77 - 84	27
84 - 91	38
91 - 98	32
98 - 105	16
105 - 112	15

Mathematics

The following are the marks obtained by 70 boys in a class test.
Marks No. of boys
30 - 40 10
40 - 50 12
50 - 60 14
60 - 70 12
70 - 80 9
80 - 90 7
90 - 100 6
Calculate the mean by :
(i) Short-cut method
(ii) Step-deviation method

Measures of Central Tendency

Related Questions

The mean of data, represented by given diagram is :
53
47
42
51

The following table gives the ages of 50 students of a class. Find the arithmetic mean of their ages.
Age (years) No. of students
16 - 18 2
18 - 20 7
20 - 22 21
22 - 24 17
24 - 26 3

Find mean by 'step-deviation method' :
C.I. Frequency
63 - 70 9
70 - 77 13
77 - 84 27
84 - 91 38
91 - 98 32
98 - 105 16
105 - 112 15

Marks	No. of boys
30 - 40	10
40 - 50	12
50 - 60	14
60 - 70	12
70 - 80	9
80 - 90	7
90 - 100	6

Mathematics

The following are the marks obtained by 70 boys in a class test.MarksNo. of boys30 - 401040 - 501250 - 601460 - 701270 - 80980 - 90790 - 1006Calculate the mean by :(i) Short-cut method(ii) Step-deviation method

Measures of Central Tendency

Related Questions

The mean of data, represented by given diagram is :53474251

The following table gives the ages of 50 students of a class. Find the arithmetic mean of their ages.Age (years)No. of students16 - 18218 - 20720 - 222122 - 241724 - 263

Find mean by 'step-deviation method' :C.I.Frequency63 - 70970 - 771377 - 842784 - 913891 - 983298 - 10516105 - 11215

The following are the marks obtained by 70 boys in a class test.
Marks No. of boys
30 - 40 10
40 - 50 12
50 - 60 14
60 - 70 12
70 - 80 9
80 - 90 7
90 - 100 6
Calculate the mean by :
(i) Short-cut method
(ii) Step-deviation method

The mean of data, represented by given diagram is :
53
47
42
51

The following table gives the ages of 50 students of a class. Find the arithmetic mean of their ages.
Age (years) No. of students
16 - 18 2
18 - 20 7
20 - 22 21
22 - 24 17
24 - 26 3

Find mean by 'step-deviation method' :
C.I. Frequency
63 - 70 9
70 - 77 13
77 - 84 27
84 - 91 38
91 - 98 32
98 - 105 16
105 - 112 15