UNIT 3-MEASURES OF CENTRAL TENDENCY

Problems

1. Compute Mean mark of 10 students in Statistics. 40, 48, 35, 59, 70, 92, 48, 68, 82 and 28
2. From the following data compute arithmetic mean (Ans: 452.26)

X 200 300 400 500 600 700 800

F 20 25 32 38 20 12 8
3. Calculate arithmetic mean (Ans: 33.572)
Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70
No. of students 5 8 15 20 12 6 4
4. Calculate the arithmetic mean from the following (Ans: 36.66)
Marks Number of students
Below 10 04

Below 20 14
Below 30 32
Below 40 54

Below 50 70
Below 60 81
Below 70 90
5. Calculate arithmetic mean (Ans: 39.8)
Income (‘000 Rs.) Number of families
More than 0 100

More than 10 95

More than 20 82

More than 30 60

More than 40 45

More than 50 36

More than 60 20

More than 70 10
6. Calculate arithmetic mean (Ans: 38.5)
Marks 0-10 10-30 30-60 60-100
Students 7 13 22 8
7. Find the missing frequency from the following data if it’s mean is 15.6 (Ans: 11)

X 10 12 14 16 18 20 22
F 2 4 8 ? 6 3 1
8. Find the missing frequency from the following data whose Arithmetic mean is 59.3 (Ans: 5 and 6)

X 40 45 50 60 70 80 100 Total
F 3 ? 16 12 6 ? 2 50
9. If the average wages paid to 25 workers is Rs.79.60, find the missing
frequencies. (Ans: 5 and 7)

Wages(Rs.) 50 60 70 80 90 100 110

No. of workers 1 3 ? ? 6 2 1
10. Find out the missing frequency from the following data, if the mean is 67.45. (Ans: 27)
Height (inches) 60-62 63-65 66-68 69-71 72-74

No. of students 5 18 42 ? 8
11. If x̅ 1= Rs.275, N1 = 100, x̅ 2= Rs.225 and N2 = 80 find x̅12. (Ans: 252.77)
12. An average monthly production of a certain factory for the first eight months is 3546 units
and for the remaining four months is 3100 units. Calculate the average monthly production
for the year. (Ans: 3397 units)
13. The combined mean height of 60 boys is 60.8cms. The mean height of the first 30 boys is
62cms and that of the last 20 boys is 6 1.2cms. Find the mean height of the remaining boys.
(Ans: 56.4cms)
14. The average daily wage of all workers in a factory is Rs.234. If the average daily wages paid
to male and female workers are Rs.240 and Rs.220 respectively, find the percentage of male
and female workers employed by the factory.
(Ans: 70% male and 30% female workers are employed)
15. The Marks scored by 50 students in an examination are given below:
30 45 48 55 39 25 31 12 18 21
54 59 51 33 43 44 10 38 19 26
47 35 37 41 46 33 51 37 58 58
17 19 23 26 29 38 57 36 35 44
43 27 31 43 22 31 47 34 18 15
Prepare a frequency table by taking a class interval of 10. Find Mean. (ans: 35.6)

16. 100 students appeared for an exam. The results of those who failed are given below.
Marks 5 10 15 20 25 30
No of 4 6 8 7 3 2
Students
If the average marks of all the 100 students is 68.6.Find out the average marks of those who have passed.

HW:
1) The mean height of 50 students in a class is 62”. The height of 30 of these is given in the frequency
distribution below. Find the mean height of remaining 20 students. (Ans: 62.4)
 Height in inches 60 61 62 63 64
No. of students 4 12 4 8 2

17) Calculate median from the following (Ans.Rs980)

House No 1 2 3 4 5 6 7
Family Income (Rs.) 980 1020 720 800 1200 600 2000
18) The prices of wheat per 40 kgs in 10 different shops arranged in an array is Rs.280,
285, 287, 290, 292, 295, 297, 305,310 and 315. Calculate median price. (Ans: Rs.293.5)
19) Determine median from the following
X 10 20 30 40 50 60 70
F 2 3 4 6 10 5 2
20) Compute median from the following (Ans: 13.846)
X 0-5 5-10 10-15 15-20 20-25 25-30
F 5 10 13 12 7 3
21) Calculate median from the following (Ans: 54.459)

NO. OF
MARK
STUDENTS
80-90 8
70-80 13
60-70 23
50-60 37
40-50 25
30-40 12
20-30 7
10-20 4

22) Calculate median (Ans: 37.143)

X F
Less than 10 5
Less than 20 15
Less than 30 35
Less than 40 56
Less than 50 79
Less than 60 91
Less than 70 98
Less than 80 100
23) Calculate median (Ans: 32.5)
Income (Rs. In ‘000) Number of families
More than 0 100
More than 10 91
More than 20 78
More than 30 54
More than 40 38
More than 50 26
More than 60 18
More than 70 10
24) Compute median from the following (Ans: 152.533)
Mid-point 115 125 135 145 155 165 175 185 195
Frequency 5 20 41 65 75 58 25 9 2
25) Find the missing frequency in the group 10-20 when the median is given to be 28 (Ans: 8)
X 0-10 10-20 20-30 30-40 40-50
F 5 ? 15 16 6
26) An incomplete distribution is given below: (Ans:33.5 & 45.5, Mean = 45.829)
X 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Total
F 12 30 ? 65 ? 25 18 229
You are told that median is 46. After filling up the missing frequencies, calculate mean.
27) Find the missing frequencies if the value of median is 43 and N = 90 (Ans: 8 and 20)
C.I 0-10 10-20 20-30 30-40 40-50 50-60 60-70
Frequency 8 12 14 ? 10 ? 18
28) The marks obtained in an exam by 20 students in a class are given. Calculate
mode.(Ans: 25)
27 25 30 35 25 30 37 41 40 25
20 23 45 26 25 38 40 36 22 21
29) Find the value of mode.
X 10 20 30 40 50 60 70 80
f 4 9 16 25 22 15 7 3
30) Find the value of mode.
X 10-20 20-30 30-40 40-50 50-60 60-70 70-80
F 6 10 12 18 11 6 3
31) Find the value of mode from the following data:
X 0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79
F 5 7 10 15 8 3 2 1
 32) From the following data on the weight of 200 police constables determine
the modal weight (Ans: 128lbs)
Weight
116 120 122 124 126 128 130 132 136 140
(in lbs)
No. of
8 12 10 29 40 44 48 12 4 2
persons

33) Calculate mode (Ans: 24)

X 0-5 5-10 10-15 15-20 20-25 25-30 30-35
F 1 3 10 6 10 9 1
34) Calculate the missing frequency when the mode = 14.714 (Ans: 13)
X 1-9 9-17 17-25 25-33 33-41
F 10 15 ? 8 6
35) Find the missing frequencies when mode = 26 and N = 50
X 0-10 10-20 20-30 30-40 40-50
F 3 ? 20 12 ?

36) Given x̅ = 21.76, M = 20.84, find Z (Ans: 19)

37) Find Median if Z = 49, x̅= 50 . 73 (Ans:50.133)
38) Calculate the value of mode by using graphical method. Also verify with actual calculation. (Ans:
35.74)
X 0-10 10-20 20-30 30-40 40-50 50-60 60-70
F 12 32 38 65 45 25 18
39) Find mode by using graphical method from the following (Ans: 22.22)
X 10-15 15-20 20-25 25-30 30-40 40-60 60-80
F 5 15 23 13 12 12 8
40) Modal marks for a group of students is 26, 14 students got marks between 0-10, 27
students between 20-30, 21 students between 30-40and 15 students between 40 and
50. Find the number of students getting between 10 and 20. (Ans: 18)
41) Draw ‘less -than ogive’ and ‘more-than ogive’ from the following data and locate
the value of median. Also verify with actual calculation. (Ans: Median=135)
Class interval 0-50 50-100 100-150 150-200 200-250
Frequency 10 30 50 40 20
42) Draw less-than cumulative frequency curve and find 1) Median, also verify
with actual calculation and find 2) persons getting wages below Rs.550 (Ans:
Median=436.84 and 212 workers)
Wages 100-200 200-300 300-400 400-500 500-600 600-700 700-800
No. of persons 24 38 50 76 48 30 14
43) Find out the mean and median marks from the following. Using empirical
relationship calculate mode (Ans: Mean=49.583, Median=58.33 and
mode=75.833)
Marks below 10 20 30 40 50 60 70 80
No. of students 25 40 60 75 95 125 190 240
 44) Find the value of mean, median and mode from the following data
(Ans: Mean=92.653, Median=92.8, and Mode=93.192)
Weight in kgs 71-75 76-80 81-85 86-90 91-95 96-100 101-105 106-110 111-115
No. of students 3 10 15 18 25 19 14 9 2