Statistics
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A value of C for which the conclusion of Mean Value Theorem holds for the function f(x) = logex on the interval [1, 3] is
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2log3e
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loge3/2
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log3e
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loge3
A.
2log3e
Using mean value theorem
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All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?
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Mean
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Median
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Mode
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Variance
D.
Variance
If initially, marks of students were xi, then
So, the variance will not change whereas mean, median and mode will increase by 10.
For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is
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5/2
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11/2
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6
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13/2
B.
11/2
If in a frequently distribution, the mean and median are 21 and 22 respectively, then its mode is approximately
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22.0
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20.5
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25.5
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24.0
D.
24.0
Mode + 2Mean = 3 Median
⇒ Mode = 3 × 22 – 2 × 21= 66 – 42= 24.
If the mean deviation about the median of the numbers a, 2a, ....., 50a is 50, then |a| equals
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2
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3
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4
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5
C.
4
Median = 25.5 a
Mean deviation about median = 50
⇒24.5 a + 23.5a + ..... + 0.5a + 0.5a + .... + 24.5a = 2500
⇒ a + 3a + 5a + ..... + 49a = 2500
⇒ 25/2 (50a) = 2500 ⇒ a = 4
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Mock Test Series
Mock Test Series