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Assertion and Reason Questions Class 9 Maths Chapter 14 Statistics
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
2) Assertion: median= ((n+1)/2)th value if n is odd
Reason: tion : If the number of runs scored by 11 players of a cricket team of India are 5, 19, 42, 11, 50, 30, 21, 0, 52, 36, 27 then median is 30
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: c) Assertion is correct but reason is false
3) Assertion: if the value of mode and mean is 60 and 66 then the value of median is 64
Reason: median= (mode+2mean)
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: c) Assertion is correct but reason is false
4) Assertion: Median of the given data 34,31,42,43,46,25,39,45,32, is 39.
Reason : When the number of observations (n) is even arrange the numbers in the ascending order then the median is the mean of the and | n+1 |
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion
5) Assertion: If mean & median of an asymmetrical distribution are 58 & 61respectively, then Mode =67.
Reason: For an asymmetrical distribution Mode =3 Median −2 Mean .
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
6) Assertion: Mean of n observations= Number of oobservations/Sum of observations
Reason: if the mean of five observations x , x + 2, x + 4, x + 6, x + 8 is 11, then mean of last three observations is 8
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: c ) Assertion is true but reason is false
7) Assertion: The median of 83, 37, 70, 29, 45, 63, 41, 70, 34, 54, is 49.5.
Reason : The median of n odd number of observations is( (n+1)/2)thterm.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion
8) Assertion: The median of the following observation 0, 1, 2, 3, x , x + 2, 8, 9, 11, 12 arranged in ascending order is 63, then the value of x is 62.
Reason : Median of n even observations is(( (n)/2)thterm+(n/2+1)th term)/2
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
9) Assertion: Range = Maximum value – Minimum value
Reason: The range of the first 6 multiples of 6 is 9.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: c) Assertion is true but reason is false
10) Assertion: The following is the data of wages per day: 8, 4, 7, 5, 8, 8, 5, 7, 9, 5, 7, 9, 10, 8, then the mode of the data is 8.
Reason : Mode = Highest observation – lowest observation
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: c) Assertion is true but reason is false
11) Assertion: mode of given data 110,120,130,120,110,140,130,120,140,120 is 120
Reason: the observation with maximum frequency is called mode
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.
12) Assertion: Median of the given data 34, 31, 42, 43, 46, 25, 39, 45, 32, is 39.
Reason : When the number of observations ( )n is even, the median is the mean of(n/2)th and(n/2+1) th observation
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.
13) Assertion: : The difference between the maximum and minimum values of a variable is called its range.
Reason : The number of times a variate (observation) occurs in a given data is called range.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: c) Assertion is correct but reason is false
14) Assertion: If the median of the given data 26, 29, 42, 53, x , x + 2, 70, 75, 82, 93, is 65 then the value of x is 64.
Reason : When the number of observations ( )n is odd the median is the value of the(( n+1)/2)th observation.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.
15) Assertion: Mean may or may not be the appropriate measure of central tendency.
Reason : If the number of observations are even then median is ((n+1)/2)th term
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: c) Assertion is correct but reason is false
16) Assertion: the median and mode of a frequency distribution are 150 and 154 respectively, then its mean is 148.
Reason: Mean, median and mode of a frequency distribution are related as: mode = (3 median) – (2 mean)
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
17) Assertion: the mode of below data is14.6
Class interval | 3-6 | 6-9 | 9-12 | 12-15 | 15-18 | 18-21 | 21-24 |
Frequency | 2 | 5 | 10 | 23 | 21 | 12 | 3 |
Reason: The value of the variable which occurs minimum often is the mode
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: c) Assertion is correct but reason is false
18) Assertion: According to statistics more female children are born each year than male children in India.
Reason : In India the death rate of a male child is higher than that of the female child.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: c) Assertion is correct but reason is false
19) Assertion: the mode of above data is12.4
Class interval | 3-6 | 6-9 | 9-12 | 12-15 | 15-18 | 18-21 |
Frequency | 2 | 5 | 21 | 23 | 10 | 12 |
Reason: the value of variable which occur most often is mode
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: b) both Assertion and reason are correct but reason is not correct explanation for assertion
20) Assertion: The ratio of the sum of observations and the total number of observations is called mean
Reason: The mean of x+2, x+3, x+4 and x-2 is (4x+7)/4
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for assertion
21) Assertion: The median of the data: 4, 6, 8, 9, 11 is 8
Reason: The median of the data: 155, 160, 145, 149, 150, 147, 152, 144, 148 is 149
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: b) both Assertion and reason are correct but reason is not correct explanation for assertion
22) Assertion: The mode of the given data: 4, 6, 5, 9, 3, 2, 7, 7, 6, 5, 4, 9, 10, 10, 3, 4, 7, 6, 9, 9 is 6
Reason: The value which appears very frequently in a data is called median
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: d) both Assertion and reason are false
23) Assertion: the class mark of the class interval 90-120 is 105
Reason: Class mark = (upper limit + lower limit)/2
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct but reason is correct explanation for assertion
24) Assertion: the class intervals 10-20, 20-30, 20 is included in which interval 20-30
Reason: the number is always included in the lower limit of the class interval.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct but reason is correct explanation for assertion
25) Assertion: the class width for the grouped frequency distribution of the class intervals 1-20, 21-40, 41-60, .. is 20
Reason: Class width is the same as the class size
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct but reason is correct explanation for assertion
26) Assertion: If each data in the observation is increased by 5, then the mean is increased by 5
Reason: the mean is the average of the given values.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct but reason is correct explanation for assertion
27) Assertion: The difference between the maximum and minimum values of the given observation is called range
Reason: the maximum value is 120 if the range is 38 and the minimum value is 82.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct but reason is correct explanation for assertion
28) Assertion:15 is the mode of 4, 4, 4, 9, 15, 15, 15, 27, 37, 48 data set.
Reason: mode is defined as the value that has a higher frequency in a given set of values.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct but reason is correct explanation for assertion
29) Assertion: If the mean of frequency distribution is 7.5 and ∑fi xi = 120 + 3k, ∑fi = 30, then k is equal to 35
Reason: X mean = ∑fi xi /∑fi
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct but reason is correct explanation for assertion
30) Assertion: The mode and mean is given by 7 and 8, respectively. Then the median is 22/5
Reason: Mode = 3 Median – 5 Mean
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: d) both Assertion and reason are false
31) Assertion: The mean of the data: 4, 10, 5, 9, 12 is 8
Reason: mean = (4 + 10 + 5 + 9 + 12)/5 = 40/5 = 8
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct but reason is correct explanation for assertion
32) Assertion: The median of the data 13, 15, 16, 17, 19, 20 is 33/2
Reason: median = (16 + 17)/2 = 33/2
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct but reason is correct explanation for assertion
33) Assertion: If the mean of first n natural numbers is 3n/5, then the value of n is 5
Reason: Sum of natural numbers = n(n + 1)/2
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct but reason is correct explanation for assertion
34) Assertion: The mean is one of the numbers in data.
Reason: The mean is one of the numbers in data.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: d) both Assertion and reason are false.
35) Assertion: The measures of central tendency lie between the maximum and minimum values of the data.
Reason: The measures of central tendency may not lie between the maximum and minimum values of data.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: c) Assertion is correct but reason is false
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion
37) Assertion: median is the middle observation of an ordered set.
Reason: 1,2,4,5,5,6,8 here middle observation is 5 , so the median is 5
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for assertion
38) Assertion: 1,3,3,6,7,8,9 here the median is 6
Reason: 1,2,3,4,6,8,9 here the median is 4
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: b) both Assertion and reason are correct but reason is correct explanation for Assertion
39) Assertion:2,4,6 here median is the 4
Reason: 2,4,6,8 here median is the 5
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion
40) Assertion: set of data with one Mode is known as a Unimodal Mode.
Reason: the Mode of data set A = { 14, 15, 16, 17, 15, 18, 15, 19} is 15 as there is only one value repeating itself. Hence, it is a Unimodal data set
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
41) Assertion: A set of data with two Modes is known as a Bimodal Mode
Reason: the Mode of data set A = { 8,13,13,14,15,17,17,19} is the example of bimodal mode
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
42) Assertion: the Mode of data set A = {2, 2, 2, 3, 4, 4, 5, 6, 5,4, 7, 5, 8} is the example of trimodal set
Reason: because all the three values are repeating thrice in the given set. Hence, it is a Trimodal data set.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
43) Assertion: the modal value for the following set of data is 16 12,14,16,18,26,16,20,16,11,12,16,15,20,24
Reason: the modal value for the following set of data are 86,88 85,86,86,88,88,90,91,95
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion
44) Assertion: If the difference between the mode and median is 2, then the difference between the median and mean is 1
Reason: Mean – Mode = 3 [ Mean – Median ]
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a)both Assertion and reason are correct and reason is correct explanation for Assertion
45) Assertion: The pre modal class and the post modal class rectangles have the same height. If the modal class is 40-60 , then the mode is 50
Reason: Mode = L +(fm−f1/(2fm−f1−f2)) × h
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a)both Assertion and reason are correct and reason is correct explanation for Assertion
46) Assertion: 13,13,13,13, 14,14,16,18,21 here range is 8
Reason: 1,2,4,7 here range is 6
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion
47) Assertion: the mean of x,y,z is y then x+z= 2y
Reason: (x+y+z)/3 = y, hence x+y+z=3y. x+z=2y
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a)both Assertion and reason are correct and reason is correct explanation for Assertion
48) Assertion: Class mark is defined as the mean of the lower limit and upper limit.
Reason : the mid point of a class interval is called the lower limit
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans:c) Assertion is correct but reason is false
49) Assertion: class mark of a class is obtained by using 1/2(upper limit- lower limit)
Reason: Class mark is the mean of the upper limit and lower limit of the class.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
50) Assertion: mean of first ten odd natural number is 10
Reason: mean of n number = sum of n number/n
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertions and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for assertion