# 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

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

Class interval | 5-15 | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 |

Frequency | 6 | 11 | 21 | 23 | 14 | 4 |

Solution:

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