CBSE Important Mathematics Questions of Class X Chapter {Statistics} for CBSE Examination 2023
1) Find the median of the data ,using an empirical relation when it is given that mode = 12.4 and mean = 10.5.
3) From the following frequency distribution, find the median class
Cost of living index
1400 – 1550
1550 – 1700
1700 – 1850
1850 - 2000
Number of weeks
8
15
21
8
Find the upper limit of the modal class.
5) In the frequency distribution, if ∑ fi = 50 and ∑ fixi = 2550.=, then what is the mean of the distribution?
6) If ∑ fi = 15, ∑ fixi = 3p + 36 and mean of the distribution is 3, then find the value of p.
7) If mode = 80 and mean = 110, then find the median.
8) Calculate the mean of first 5 prime numbers.
9) In the data, the difference between mode and the mean is k times the difference between median and mean, then find the value of k.
10) Given blow is the distribution of weekly pocket money received by students of the class. Calculate the pocket money that is received by most of the students.
Pocket Money
0 – 20
20 – 40
40 – 60
60 – 80
80 – 100
100 – 120
120 - 140
No. of students
2
2
3
12
18
5
2
12) Find the value of λ, if th mod of the following data is 20.
15, 20, 25, 18, 13, 15, 25, 15, 18, 17, 20, 25, 20, λ, 18
13) Find the mean of the following distribution:
Class Interval
0 – 6
6 – 12
12 – 18
18 – 24
24 – 30
Frequency
5
4
1
6
4
14) Find the mean of the following frequency distribution:
Xi
3
4
5
7
10
Fi
3
4
8
5
10
15) Using the formula connecting mean, median and mode, find the median, when mode is 43 and mean is 34.
16) The distribution of sale of shirts sold in a month in a departmental store is as under. Calculate the modal size of the shirts sold.
Size (in Cm)
80 – 85
85 – 90
90 – 95
95 – 100
100 – 105
105 – 110
110 – 115
No. of Shirts sold
33
27
85
155
110
45
15
17) An aircraft can have 120 passengers. The number of seats occupied during 100 flights is given in the following table: Determine the mean number of seats occupied over the flights.
No. of Seats
100 – 104
104 – 108
108 – 112
112 – 116
116 – 120
Frequency
15
20
32
18
15
18) Calculate the median from the following data:
Marks
0 – 10
10 – 20
20 – 30
30 – 40
40 – 50
No. of Students
5
15
30
8
2
19) The following distribution shows the marks scored by 140 students in an examination. Calculate the mode of the distribution.
Marks
0 – 10
10 – 20
20 – 30
30 – 40
40 – 50
No. of Students
20
24
40
36
20
20) Write the relationship connecting three measures of central tendencies. Hence, find the median of the given data if mode is 24.5 and mean is 29.75.
21) Find the mode of the following frequency distribution.
Classes
0 – 6
6 – 12
12 – 18
18 – 24
24 – 30
Frequency
7
5
10
12
6
22) Find the mean of the following data:
Classes
0.5 – 5.5
5.5 – 10.5
10.5 – 15.5
15.5 – 20.5
20.5 – 25.5
Frequency
13
16
22
18
11
24) The weekly expenditure of 500 families is tabulated below: Find the median Expenditure.
Weekly Expenditure
0 – 1000
1000 – 2000
2000 – 3000
3000 – 4000
4000 – 5000
No. of families
150
200
75
60
15
25) The weight (in kg) of 45 students of a class are given in the following distribution table. Determine the value of weight x which is such that the number of students having weight less than x kg is same as the number of students having weights more than x kg.
Weight
Below 45
Below 50
Below 55
Below 60
Below 65
Below 70
Cumulative frequency
5
11
15
22
38
45
26) The mean of following distribution is 48 and sum of all the frequencies is 50. Find the missing frequencies x and y.
Class
20 – 30
30 – 40
40 – 50
50 – 60
60 – 70
Frequency
8
6
X
11
y
27) The given frequency distribution represent the number of passengers who boarded a local bus during a particular day.
Time
5 – 8
8 – 11
11 – 14
14 – 17
17 – 20
20 – 23
No. of Passengers
40
90
44
58
53
10
28) Find the median of following data:
Height
Less than 120
Less than 140
Less than 160
Less than 180
Less than 200
No. of Students
12
26
34
40
50
29) The mean of the following data is 21, find the value of p.
Class
7.5 – 12.5
12.5 – 17.5
17.5 – 22.5
22.5 – 27.5
27.5 – 32.5
32.5 – 37.5
Frequency
6
10
P
10
2
8
30) The following frequency distribution gives the marks of students in a class test:
Marks
0 – 10
10 – 20
20 – 30
30 – 40
40 – 50
No. of Students
10
24
38
22
6
Using step deviation method to find the mean marks.
31) The mean of the following frequency distribution is 25.2. Find the missing frequency x.
C.I
0 – 10
10 – 20
20 – 30
30 – 40
40 – 50
Frequency
8
X
10
11
9
32) The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and the mode of the data and the compare them.
Monthly Consumption
65 – 85
85 – 105
105 – 125
125 – 145
145 – 165
165 – 185
185 – 205
No. of consumers
4
5
13
20
14
8
4
33) If the median of the distribution given below is 27. Find the values of x and y.
Class
0 – 10
10 – 20
20 – 30
30 – 40
40 – 50
50 – 60
Frequency
5
X
20
14
Y
8
34) Find the missing frequencies in the following frequency distribution table, if n = 100 and median is 32.
Marks
0 – 10
10 – 20
20 – 30
30 – 40
40 – 50
50 – 60
No. of students
10
?
25
30
?
10
35) If the mean of the following data is 14.7, find the value of P and Q.
Class
0 – 6
6 – 12
12 – 18
18 – 24
24 – 30
30 – 36
36 – 42
Frequency
10
P
4
7
Q
4
1
36) The mean of the following data is 50, Find the missing frequencies f1 and f2.
Class
0 – 20
20 – 40
40 – 60
60 – 80
80 – 100
Frequency
17
F1
32
F2
19
37) Draw a “less than ogive” for the following distribution:
Class
5 – 8
8 – 10
10 – 12
12 – 14
14 – 16
16 – 18
Frequency
60
50
70
150
80
90
38) Draw “more than ogive” for the following frequency distribution and hence obtain the median:
Class
5 – 10
10 – 15
15 – 20
20 – 25
25 – 30
30 – 35
35 – 40
Frequency
2
12
2
4
3
4
3
39) Following data was obtained regarding concentration of sulpher dioxide (SO2) in the air in 24 localities of a city.
Concentration of SO2 (in ppm)
0.00 – 0.02
0.02 – 0.04
0.04 – 0.06
0.06 – 0.08
0.08 – 0.10
0.10 – 0.012
Frequency
2
5
4
3
4
6
(i) Find the mean concentration of SO2 in the air.
(ii) What idea is indicated from this action?
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