NCERT Class 10 Mathematics Statistics Formative assessment CBSE Board Sample Problems Part 1

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Fill in the blank

(a) The mean of 50 numbers is 18, the new mean will be.... if each observation is increased by 4 (22/24/20)

Solution

(a) 24

Now when each number is increased by 4, we have

So M=22

(b) The sum of deviations of a set of values n items measured from 26 is -10 and the sum of deviations of the values from 20 is 50. The value of n is. ..(10/1219) And mean of the items is (19/18/17/25)

Solution:

10, 25

Subtracting, we get

(c) For a given data with 110 observations the ‘less than ogive’ and the ‘more then ogive’ intersect at (18, 20). The median of the data is (18/20/19)

Solution:

18. Median is the point of intersection of ogive curves

(d) The curve drawn by taking upper limits along x-axis and cumulative frequency along y-axis is (less than ogive /more than ogive)

Solution: less than ogive curve

(e) The mean of five numbers is 40. If one number is excluded, their mean becomes 28. The excluded number is (68 / 88)

Solution: 88

Sum of five number

Sum of four number

Subtracting, we get the number

(f) The modal class of the grouped size frequency table given below is

The modal class of the grouped size frequency table given below is

5-5.2

5.2-5.4

5.4-5.6

5.6-5.8

5.8-6.0

34

4

4

4

6

Solution: Modal class is 5-5.2

True or False statement

The following shows the class interval

The following shows the class interval

Class interval

5-15

15-25

25-35

35-45

45-55

55-65

Frequency

6

11

21

23

14

4

Solution:

Table Supporting: NCERTClass10MathematicsStatisticsFormativeassessmentCBSEBoardSampleProblemsPart1

Class interval

5-15

15-25

25-35

35-45

45-55

55-65

Frequency

6

11

21

23

14

4

Class mark

10

20

30

40

50

60

60

220

630

920

700

300

Mean is given by

The class having highest frequency is called the Modal class, so Modal class is 35-45

Where

l= lower limit of the modal class,

h = size of the class interval (assuming all class sizes to be equal),

= frequency of the modal class,

= frequency of the class preceding the modal class,

= frequency of the class succeeding the modal class.

Now and

So substituting all the values, we get

Mo=36.81

Now

3 Median= Mode +2 Mean

So median

a) The mean is 33

Solution: False

b) The modal class 35-45

Solution: True

c) The mode is 34

Solution: False

d) The Frequency for less than is 35 is 38

Solution: True

e) The median is

Solution: False