Central
Tendency
1. Find out the mean from the following data:
Age(year): 10, 28, 37, 45, 25, 36, 50.
2. Calculate Arithmetic mean from the following data:
Daily Wages(in taka) : 50 60
80 90
120 150
No of workers :
5 7 12
15 8 3
3. Calculate Arithmetic Mean from the following data:
Marks : 0-10 10-30 30-60 60-100 100-120
No of Students :
5 12 25 8 3
4. Find out the mean from the following data:
Daily Wages(in taka) : 10-20 20-30 30-40
40-50 50-60
No of workers :
5 10
15 20 10
5. Calculate Arithmetic mean from the following
frequency distribution :
H.W Marks
: 10-19 20-29 30-39 40-49 50-59 60-69
No of Students:
10 17 30 51 29 9
6. Calculate Arithmetic Mean from the following frequency distribution
: H.W
Monthly
Salary(in tk)
Number of Workers
500 but less than 600 4
600 but less than 700 10
700 but less
than 800
14
800 but less
than 900 12
900 but less
than 1000 4
1000 but less than
1100
2
7. Honours Coaching Center wants to pay bonus
to the numbers of staffs. The bonus is to paid as follows
Monthly
Salary (in tk) Bonus ( in
tk)
1000 and not exceeding 1200 500
1200 and not
exceeding 1400
600
1400 and not exceeding 1600 700
1600 and not exceeding 1800 800
1800 and not exceeding 2000 900
2000 and not exceeding
2200 1000
2200 and over 1100
Actual salary of the numbers of staff is given unders
:
1100,
2000, 1800, 1950,
2180, 1870, 1600,
1500, 1980, 1680,
1700, 1780, 1750,
1100, 1200, 1480,
1550, 2450, 1250,
1100, 1620, 1300,
1500, 1850.
Req: 1) What is
the total bonus paid ?
2) What
is the average bonus paid ?
8. A company limited wants to
pay bonus to the members of staff . The bonus is to be paid as follows : H.W
Monthly
Salary (in tk) Bonus ( in
tk)
300 and
not exceeding 400
100
400 and not
exceeding 500 120
500 and not exceeding 600
140
600 and not exceeding 700 160
700 and not exceeding 800 180
800 and not exceeding 900
200
900 and not exceeding 1000 220
1000 and not
exceeding 1100
240
Actual Salary of the members of the staffs is given unders:
tk. 325, 378,
420, 620, 455,
620, 660, 680,
725, 863, 832,
942, 952, 800,
1002, 1025, 1100,
610, 625, 736,
382, 540, 463,
578, 723, 690,
Req: 1) How much the company would need to pay by way of bonus ?
2) What shall be the average
bonus paid per workers ?
Combined
Mean
9. There are two branches of a company employing 100
and 80 respectively . If Arithmetic
mean of
the monthly salaries paid by two
branches are tk. 4570 and 6750 respectively.
Find out the A.M of the
salaries of the employees of the company as a hole.
10. There are three sections in B.B.S Honours 3rd year in a certain
college. The numbers of students in each sections and the average marks obtain
by them in the paper of business statistics in the annual examination are as
follows: H.W
Section Average Marks of B.S No of Students
A
75
50
B
60
60
C
55
55
Find out the average marks obtained by the students of
three sections taken
11. The mean weight of 150 students in a certain class
in 60kg. The mean weight of boys in the class is 70kg and the girls is 55kg.
Find out the numbers of boys and the numbers of girls in the class. H.W
12. The mean marks in Statistics of 100 students of a
class was 72. The mean of marks of boys 75,While there numbers was 70. Find out
the mean marks of the girls in the class.
13. The mean of a combined groups of men and women is
30 years. If mean is of the groups of the men is 32 and that of women is 35.
Find out the (%) of men and women in the groups.
14. The average monthly wages of all workers in a
factory is tk. 444 . If the average wages is paid to male and female workers
are tk. 480 and tk.360 respectively. Find out the percentage male and female
workers by the company. H.W.
15. The average weekly wages for a groups of 25
persons working in a factory was calculated to be tk. 378.4. It was later
discovered that one figure was misread as 160 instead the correct value is tk.
200. Calculated the correct average weight.
16. The mean marks of 420 students were found to be 70. Later on it was
discovered that a score of 45 was misread as 34. Find the correct mean
corresponding to correct mean. H.W.
17. The mean of 200 observations was 50. Latter on it
was discovered that two observations were wrongly read as 92 and 80 instead of
192 and 88. Find out correct mean.
18. The mean salary paid to 10000 employees in a factory was to be tk.
2804. Latter on it was discovered that the wages of two employees was wrongly
taken as 2970 and 3650 instead of 3650 and 4650. Find out correct mean. H.W
Median
1. Calculate median from the following data.
29
54 57 33
70 61 86
72 88
2. Calculation median from the following data.
Marks
: 5 7 10 12 15 18 20
No of Students
: 6 4 8
1 7 3 4
3. Calculation median from the following Frequency
distributions :
Class Interval : 30-40 40-50
50-60 60-70 70-80
Frequency
: 2 6 18 10 8
4. Calculation median from the following frequency
distributions:
Marks
: 20-29 30-39 40-49 50-59 60-69
No of Students :
16 31 50 20 8
5. Calculation
median from the following frequency distributions:
Class intervals
: 0-100 100-250 250-500 500-600 600-700
Frequency
: 5 7 30 15 10
6. Calculation median from the following data . H.W
290 544
576 331 704
617 864 722
880 550
7. Calculation median from the following data:
Marks
: 55 70 100 122 100 50 20
No of students : 4 6 8 12 7
3 2
8. Calculation median from the following frequency
distributions .H.W
Class Interval
: 10-20 20-30 30-40 40-50
Frequency
: 8 11 18 10
9. Calculation median from the following frequency
distributions. H.W
Marks
: 10-29 30-49 50-59 70-89
90-109
No of Students :
16 31 50 20 8
10. Calculation median from the following Frequency
distribution.
Class intervals : 0-10 10-25 25-50 50-60 60-70
Frequency
: 5 7 30 15 10
11. 5% of the workers in a firm employing a total of
2000 workers earn less than tk.2.00 per hour, 480
earn form
tk.2.00 to tk.2.24 per hour , 35% earn from tk.2.25 to tk.2.49 per hour. 370
earn from
tk.2.50
to tk.2.74 per hour, 12% earn form tk.2.75 to tk.2.99 per hour and rest earn tk.3.00 to tk.
more per
hour. What is the median of wages.
12. 10% of workers in a firm employing a total of 1000
workers earn less than tk.5.00 per day, 200 earn
between
tk.5.00 and tk.10 per hour, 30% earn form tk.10 and tk.15 , 250 earn between
tk. 15 and
tk.20 per
hour and rest tk.20 and above. What is the median wages.
13. Calculation median from the following frequency
distributions patterning to the profits tk(core) of 125
companies:
Profits (tk core)
Numbers of
Companies
Less than 10 4
Less than 20 16
Less than 30 40
Less than 40 76
Less than 50 96
Less than 60 112
Less than 70 120
Less than 80 125
Geometric Mean
1. Calculation Median from the following
data.
29
54 57 33 70 61 86 72 88
2. Calculation median from the following data.
Marks
: 5 7 10 12 15 18 20
No of Students
:6 4 8 1 7 3 4
2. Calculation median from the following
Frequency distribution:
Class Interval
: 30-40 40-50 50-60 60-70 70-80
Frequency
: 2 6 18 10 8
Harmonic Mean
1. Calculation median from the following
data :
290 544 576
331 704 617
864 722 880
550
2. Calculation Median from the following data :
Marks :
55 70 100
122 100 50
20
No of students :
4 6 8
12 7 3
2
3
Calculation
median from the following Frequency distribution.
Class interval : 10-20 20-30
30-40 40-50 50-60
Frequency
: 8 11 18 10 8
Quartiles , Deciles
percentiles and Mode
1.Calculation quartiles ( 1st & 3rd
) from the following data :
29,
54, 57,
33, 70, 61,
86, 72, 88
2. Calculation Quartiles ( 1st & 3rd
) from the following frequency
distribution :
Daily Wages
( in tk) : 50, 60,
80, 90, 120, 150,
No of workers :
5, 7, 12, 15, 8, 3
3.Find out the quartiles ( 1st & 3rd
) from the following data :
Daily Wages ( in tk) : 10-20 20-30 30-40 40-50 50-60 60-70
No of Workers
: 5 10 15 20 10 5
4.Calculate Quartiles ( 1st & 3rd)
From the following frequency distribution :
Marks :
10-19 20-29 30-39 40-49 50-59 60-69 70-79
No of
stu : 10 17 30 51 29 9 5
5. Calculate D1,D3, & D5 from the following
frequency distribution :
29 20 54 88 61 91 72 86 70 39
6. Calculation Deciles ( D4, D7, & D9) from the
following frequency distribution :
Marks :
55 70 100 122 100 50 20
No of stu
: 4 6 8 12 7 3 2
7. Calculation Deciles ( D1,D4, & D9) from the
following frequency distribution :
Class
Interval : 10-20 20-30 30-40 40-50 50-60
Frequency : 8 11 18 10 4
8. Calculate Deciles ( D1, D5 & D9) from the
following frequency distribution :
Marks : 10-29 30-49 50-69 70-89 90-109
No of
stu :
16 31 50 20 8
9. Calculation 2nd Quartiles , D4 and D7
from the following frequency distribution :
Marks : 5 7
10 12 15 18 20
No of
stu : 6 4 8 10 7 3 4
10. Calculation median, Quartiles and Deciles ( D4
& D6) from the following frequency distributions :
Class
intervals : 0-10
10-25 25-50 50-60 60-70 70-100
Frequency : 5 7 30 15 10 2
11. From the following data draw the ogive and
determine the median, 1st & 3rd Quartiles & 4th deciles
from it.
And verify the result by formula:
Class interval : 40-44 45-49 50-54 55-59 60-64 65-69
Frequency
: 3 5 7 11 9 7
12. Calculation percentiles ( 40th & 65th
) from the following data :
29,
54, 57, 33,
70, 61, 86,
72, 88
13. Calculation 25th and 69th
percentiles from the following data :
Marks
: 55 70 100
122 100 50
20
No of student : 4
6 8 12 7 3
2
14. Find out the percentiles 60th and 90th
from the following data :
Daily Wages( in tk.)
: 10-20 20-30 30-40
40-50 50-60 60-70
No of Workers
: 5 10
15 20 10 5
15. Calculate percentiles 70th and 10th
from the following frequency distribution :
Marks
:10-19 20-29 30-39 40-49 50-59 60-69 70-79
No of stu
: 10 17 30 51 29 9 5
16. The profits earned by 100 companies during
2005-2006 are given below :
Profits : 20-30
30-40 40-50 50-60
60-70 70-80 80-90
No of companies :
4 8 18
30 15 10 8
17. A frequency distribution of the length of
Telephone calls monitored at the switch board of an office is given bellow:
Last of
Calls ( in Min's) No of Calls
0 and under 2 10
2 and under 4 25
4 and under 6 20
6 and under 8 40
8
and under 10 5
1)
Calculation the arithmetic mean of the calling time
2)
Determine and explain the meaning of 75% percentiles of the distribution.
18. From the following table showing the wages distribution
on a certain a factory :
Weekly Wages
( in take) No of companies
120-140 8
140-160 12
160-180 20
180-200 30
200-220 40
220-240 32
240-260 18
260-280 7
280-300 6
300-320 4
1) Determine the percentage of workers who earned
between tk 175 and tk 225
2) The percentage of workers who earned more than tk
250 per week
3) The percentage of workers who earned less than tk
200 per week
19.
The following relates to the wages of
150 employees in a certain companies :
Wages ( in take) No of Employees
20-25 7
25-30 18
30-35 20
35-40 40
40-45 30
45-50 10
50-55 15
55-60 10
1) Calculation the wages limit for the middle 50% of
the wages employees.
2) Calculation the wages limit for the middle 20% of
the wages employees.
20.
Calculation the mode from the following frequency distribution :
Marks
: 3 4 7 8 9 10
No of stu :
5 10 25 15 10 3
21.
Calculation mode from the following frequency distribution :
Marks :
20-30 30-40 40-50 50-60 60-70 70-80
No of stu : 7 13 20 23 25 2
22.
The following table gives the daily wages distribution of employees of a
commercial organization
Daily Wages
: 250-300 300-350 350-400 400-450 450-500 500-550 550-600
No of emm : 25 30 55 67 39 14 10
1) Compute arithmetic mean and median of the
distribution 2) Find the wages range
of the 50%
employees 3)
It is decided to collect tax from those having income of tk 530 ad avobe . What
(%)
of the employees are taxable.
23. The weekly income distribution of 600 families are given below :
Weekly income ( in take) No of families
Below -300 69
300-600 167
600-900
206
900-1200 65
1200-1500 58
1500-1800 25
1800- avobe 10
1) Find out the limit of the weekly income
of central 50% families .
2) It is decides to collect tax from those
families having income tk1400 and above. What (%) of the families are taxable
3) Find out the mean , median and mode
4) The percentages of families who earned
less than tk375 and tk1225
5) The percentages of families who earned
above tk1200
Missing Frequency
1. From the following data find out the
missing frequency when mean is 30.76
Marks
: 20 24 28
32 36 40
No of student : 3
7 ? 20
8 5
2. From the following data find out the
missing frequency when mean is 28
Class Interval : 0-10 10-20
20-30 30-40 40-50
50-60
Frequency
: 12 18 27 ? 17 6
3. From the following data find out the
missing frequency when median is 46.
Marks :10-20
20-30 30-40 40-50 50-60 60-70 70-80 Total
No of stu : 12 30 ? 65 ? 25 18 229
4. From the following data find out the
missing frequency when median is 35
Marks : 0-10 10-20
20-30 30-40 40-50
50-60 60-70 Total
Students : 10 30 ? 40 ? 25 15 170
5. The expenditure of 1000 families is
given below :
Expenditure
: 40-59 60-79
80-99 100-119 120-139
No of families :
50 ? 500 ? 50
Find out the missing frequency. Mode of the frequency
is 87.50.
6. The Exp of 100 families is given below :
Exp : 0-10 10-20
20-30 30-40 40-50 Total
No of fam :
14 ? 26 ? 15 100
Find out the missing frequency. Mode of the frequency
is 24.
7. The expenditure of some families is
given below :
Expenditure
: 0-10 10-20
20-30 30-40 40-50
No of families
: 14 ? 30 ? 6
Find out the missing frequency. Mode of the frequency
is26 and
24.
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