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