Worksheet For Dspersion

Measure of Dispersion
practice questions
1. A sample of college students was asked how much they spent monthly on a cell phone
plan (to the nearest dollar).
Monthly Cell Phone Plan Cost ($) Number of Students
10 - 19 8
20 - 29 16
30 - 39 21
40 - 49 11
50 - 59 4
Find range, and quartile deviation.
2. The following table represents the distribution of the annual number of days over 100
degrees Fahrenheit for Dallas-Fort Worth for a sample of 80 years from 1905 to 2004.
Days Above 100 Degrees Number of Years
0-9 25
10 - 19 33
20 - 29 14
30 - 39 5
40 - 49 2
50 - 59 1
Find the mean deviation from mean and median.

3. The following table shows the distribution of the number of hours worked each week (on
average) for a sample of 100 community college students.
Hours Worked per Week Number of Students
0-9 24
10 - 19 14
20 - 29 39
30 - 39 18
40 - 49 5
Find (i) quartile deviation, (ii) mean deviation from median

4. A maintenance manager has recorded the time taken by maintenance staff to repair a
particular type of equipment fault. The following table shows the time taken in minutes to
repair 250 recent faults.
Time taken Frequency
minutes
0-9 28
10 - 19 54
20 - 29 81
30 - 39 57
40 - 49 23
50 - 59 6
60 -69 1
Calculate range, quartile deviation
5. The following data on earnings in a company are supplied.

Daily earnings Rs. Number of employees
40 -49 2
50 -59 15
60 -69 21
70-79 30
80-89 20
90 -99 9
100-109 3
Calculate the following from these data.
The mean deviation from mean, The mean deviation median
6. Find the variance and the standard deviation for the frequency distribution of the data. The
data represent the average profitability of the sales outlet (in Rs.) during one week.
Class Frequency
5.5-10.5 1
10.5-15.5 2
15.5-20.5 3
20.5-25.5 5
25.5-30.5 4
30.5-35.5 3
35.5-40.5 2
7. Find the standard deviation of the following ungrouped data with frequency.
Number of
Weight of students (kg)
students (frequency)
25 15
26 20
27 25
28 30
29 30
30 20
31 10
8. Find variance and standard deviation for the following data:
Size of orders 20- 30 30- 40 40 -50 50- 60 60- 70

No. of orders 3 8 12 6 1
9. Weekly hours of work per week of full time employees in non-manual occupations are:
Hours (for men) Men Hours (for women) Women
34 6 34 10
36 18 36 24
40 56 40 59
44 9 44 5
48 5 48 2
50 2 50 3
52 4 52 1
(i) Which gender has long working hours?

(ii) Which data has less variation in working hour (using coefficient of mean deviation from
mean)?
10. Lifetime of bulbs by produced by two factories A and B are given below:
11.
12.
13. Find the coefficient of quartile deviation for each data.
14. Find the standard deviation by the transform formula (change of origin and scale)
15. Find the standard deviation by the transform formula (change of origin and scale)
16. The weight of coffee in 70 jars is shown in the following table. Determine the variance
and standard deviation.
Weight (in grams) Frequency
200-201 13
201-202 27
202-203 18
203-204 10
204-205 1
205-206 1
17. A patient’s blood pressure measured daily over several weeks averaged 182 with a
standard deviation of 12.6, while that of another patient averaged 124 with a standard
deviation of 9.4. Which patient’s blood pressure is relatively more variable?
18. The weights of three items X, and Y vary independently and have the following means
and standard deviations.
# Mean weight (kg) Standard deviation (kg)
X 10 2
Y 14 2
Calculate which item is more dispersed.
19. Mean and standard deviation of 100 items are 50 and 4, respectively. Find the sum of all
the item and the sum of the squares of the items.
20. A company owns two retail outlets. The weekly sales of the two stores during the past
five years is as follows:
Weekly sales Rs. in 000 Number of weeks
Store- I Store- II
11-15 25 15
16-20 40 20
21-25 90 60
26-30 55 150
31-35 50 15
Compute the coefficient of variation and find out which store has more stable sales.
21. The following table gives the distribution of expenditure on food per month among
working class families in two localities. Find the coefficient of mean deviation from
median of expenditure of both places and find which place is less variate in expenditure.
Rate of expenditure No of families

in rupees per month Place A Place B
1300-1600 26 40
1600-1900 300 290
1900-11200 400 900
11200-11500 215 200
11500-11800 60 50
11800-12100 20 25
12100-12400 5 10
22. Goals score by two teams A and B in a football season were as follows:
No. of goals No. of matches
score in a Team A Team B
match
0 27 17
1 9 9
2 8 6
3 5 5
4 4 3
Which team may be considered more consistent?
23. A patient’s blood pressure measured daily over several weeks averaged 182 and with a
standard deviation of 12.6. while that of another patient averaged 124 with a standard
deviation of 9.4. which patient’s blood pressure is relatively more variate?
24. A manufacturer of television tubes has two types of tubes, A and B respectively, the tubes
have mean lifetime of 1495 hours and 1875 hours and standard deviation of 280 hours and
310 hours. Which tube has the greater (i) absolute dispersion (ii) relative dispersion?
25. An analysis of monthly wages paid to workers in two firms A and B belonging to the same
industry gives the following results:
Firm A Firm B
No. of wage earners 586 648
Average monthly wage in Rs. 52.6 47.5
Variance of wages 100 121
26. A group of 7-year old boys has a mean height of 45 inches with S.D of 2.5 inches; as mean
weight of 50 pounds with a S.D of 6 pounds. In which trait is this group more variate?
27. In automobile salesman made profit of $245 on a subcompound model for which the
average profit has been $200 with S D of $50. Late on the same day he made a profit of
$620 on a large luxury model for which the average profit has been $500 with S D of $150.
For which of these models is the salesman’s profit relatively higher? For which of these
models is the salesman’s profit relatively lower dispersed?

Worksheet For Dspersion

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Measure of Dispersion

Find range, and quartile deviation.

Find the mean deviation from mean and median.

Find (i) quartile deviation, (ii) mean deviation from median

5. The following data on earnings in a company are supplied.

8. Find variance and standard deviation for the following data:

Size of orders 20- 30 30- 40 40 -50 50- 60 60- 70

Hours (for men) Men Hours (for women) Women

(i) Which gender has long working hours?

Calculate which item is more dispersed.

Rate of expenditure No of families

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