B U ACADEMY
NUMERICAL SHEET ( STATISTICS )
Class 11 - Economics
MEAN
1. Wage rate of 19 workers is given below [4]
Wages (in Rs.) 10 20 30 40 50
Number of Workers 4 5 3 2 5
A
Calculate arithmetic mean using direct , shortcut & step deviation method.
OR
HW
Sonia has annual income of Rs 1,00,000 while Mr. Sanju has annual income of Rs 80, 00,000. The average income of
Sonia and Sanju is Rs 45,00,000 per annum. Do you think average income reflects the correct picture of the life of
Sonia and Sanju?
2. Calculate arithmetic mean with the help of following data using step deviation method. [4]
AD
Marks (Less than) 10 20 30 40 50 60
Number of Students 3 10 20 25 28 30
TW
OR
Calculate arithmetic mean with the help of following data using step deviation method.
Marks (More than) 0 10 20 30 40 50
Number of Students 30 27 20 10 5 2
I
3. Following is the monthly income of eight families in a locality [4]
UD
Monthly Income (₹) : 70, 10, 500, 75, 13, 250, 8, 42
Find out arithmetic mean using Direct Method and Short-cut Method.
4. The mean of the given distribution is Rs.425. Find the missing frequency. [4]
Wages (Rs.) Number of Workers
100-200 12
200-300 8
300-400 20
400-500 32
500-600 x
600-700 8
700-800 5
MEDIAN
1/5
Udit Wadhwa
5. Calculate the median of the following frequency distribution. [4]
Salary (in Rs.) 40 45 48 50 55 60
Number of Labourers 5 7 6 10 5 8
6. Calculate median wages from the following data. [4]
Daily Wages (in Rs.) 50-59 60-69 70-79 80-89 90-99
Number of Workers 15 40 50 60 45
7. Graph the following data in the form of 'less than' and 'more than' ogives; and calculate the median value [4]
through the graph:
Marks 0−5 5−10 10−15 15−20 20−25 25−30 30−35 35−40
Number of Students 7 10 20 13 17 10 14 9
8. Weight of eight students in kg is noted as, [4]
71, 72, 64, 68, 70, 76, 73, 75
A
Find the median weight.
HW
9. If the median of a distribution given below is 28.5, then find the value of x and y. [4]
CI 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 Total
Frequency 5 x 20 15 y 5 60
Section C
AD
10. Find out mode from the following data. [4]
Size 0-4 4-6 6-10 10-15 15-20 20-30 30-35 35-40
Frequency 2 4 3 5 2 20 6 8
TW
OR
The following data-set gives mid-values and frequencies. Calculate its mode.
Mid-value 5 10 15 20 25 30 35 40 45
Frequency 7 13 19 24 32 28 17 8 6
I
UD
11. Weight of 50 students is given below. Calculate mode. [4]
Weight (in kg) 48 49 50 51 52 53
Number of Students 4 10 20 11 3 2
12. Calculate the value of mode graphically from the following data. [4]
Marks 0-5 5-10 10-15 15-20 20-25 25-30
Number of Students 6 10 20 12 8 4
OR
Identify the mode for the following data set:
21, 19, 62, 21, 66, 28, 66, 48, 79, 59, 28, 62, 63, 63, 48, 66, 59, 66, 94, 79, 19 94
13. Present the following information in the form of a histogram and locate the modal value. Give a cross-check to [4]
your answer, calculating mode through its standard formula.
Class Interval 0−10 10−20 20−30 30−40 40−50 50−60 60−70
Frequency 4 8 14 20 30 15 6
2/5
Udit Wadhwa
Section D
14. Calculate the coefficient of rank correlation from the following data: [4]
X 48 33 40 9 16 16 65 24 16 57
Y 13 13 24 6 15 4 20 9 6 19
15. In a dance competition, two judges accorded following ranks to the 10 participants. [4]
Judge X 1 2 3 4 5 6 7 8 9 10
Judge Y 10 6 5 4 7 9 8 2 1 3
Calculate coefficient of rank correlation.
16. Calculate the correlation coefficient between X and Y and comment on the relationship. [4]
X -3 -2 -1 1 2 3
Y 9 4 1 1 4 9
17. Find out rank difference correlation of X and Y [4]
A
X 80 78 75 58 67 60 59
HW
Y 12 13 14 14 16 15 17
18. Calculate coefficient of correlation by shortcut or step-deviation method between the price and quantity [4]
demanded.
AD
Price(in Rs) 5 10 15 20 25
Demand(in kg) 40 35 30 25 20
19. Following are the heights and weights of 10 students of class XI. [4]
TW
Height (in inches) Weight (in kgs)
X Y
62 50
I
72 65
UD
68 63
58 50
65 54
70 60
66 61
63 55
60 54
70 65
Draw a scatter diagram and indicate whether the correlation is positive or negative.
20. From the following data, calculate Karl Pearson’s coefficient of correlation by actual-mean method. [4]
X 6 2 10 4 8
3/5
Udit Wadhwa
Y 9 11 ? 8 7
Arithmetic mean of X and Y series are 6 and 8, respectively.
Section E
21. Construct the consumer price index number for 2011 on the basis of the following data using family [4]
budget method.
Items Price in 2000 (Rs.) Price in 2011 in (Rs.) weight
Food 200 280 30
Rent 100 200 20
Clothing 150 120 20
Fuel and lighting 50 100 10
Miscellaneous 100 200 20
A
22. Construct index number of price from the data given below by applying [4]
i. Laspeyre's Method
HW
ii. Paasche's Method
iii. Fisher's Method
Base Year Current Year
Commodity
AD
Price (in Rs.) Quantity Price (in Rs.) Quantity
A 2 40 3 20
B 1.5 30 2.5 40
TW
C 1 50 1.5 30
D 2.5 20 2 80
23. Calculate the weighted average of price relative index for 2016 on the basis of 2012 from the following data. [4]
I
p0 p1
UD
Commodity W
2012 2016
A 10 15 20
B 8 10 12
C 6 5 8
D 6 10 13
E 4 4 5
24. Construct the index number by simple average of price relative method and by simple aggregative method. [4]
Commodity A B C D E
Price in 2014 (Rs.) 16 40 35 5.25 2
Price in 2015 (Rs.) 12 60 50 6.25 1.5
25. Calculate weighted aggregative price index from the following data using Fisher's method. [4]
4/5
Udit Wadhwa
Commodity Base Year Current Year
Price (Rs.) Quantity Price (Rs.) Quantity
A 2 10 4 5
B 5 12 6 10
C 4 20 5 15
D 2 15 3 10
A
D HW
WA
IT
UD
5/5
Udit Wadhwa
