The mean of the data set comprising of 16 observations is 16. If

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 Multiple Choice QuestionsMultiple Choice Questions

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1.

The mean of the data set comprising of 16 observations is 16. If one of the observation value 16 is deleted and three new observations valued3,4 and 5 are added to the data, then the mean of the resultant data is

  • 16.8

  • 16.0

  • 15.8

  • 15.8


D.

15.8

Given, 

fraction numerator straight x subscript 1 space plus space straight x subscript 2 space plus space straight x subscript 3 space plus space..... space plus space straight x subscript 16 over denominator 16 end fraction space equals space 16
rightwards double arrow space sum from straight i space equals space 1 to 18 of straight y subscript straight i space equals space left parenthesis 16 space straight x space 16 minus 16 right parenthesis space plus space left parenthesis 3 plus 4 plus 5 right parenthesis space equals space 252
Number space of space obsercvations space space equals space 18
therefore comma space New space mean space equals space fraction numerator begin display style sum from straight i space equals 1 to 18 space of space straight y subscript straight i end style over denominator 18 end fraction
space equals space 252 divided by 18 space equals space 14

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2.

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?

  • Mean

  • Median

  • Mode

  • Mode

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3.

If the mean deviation about the median of the numbers a, 2a, ....., 50a is 50, then |a| equals 

  • 2

  • 3

  • 4

  • 4

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4.

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

  • 5/2

  • 11/2

  • 6

  • 6

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5.

If the mean deviation of the numbers 1, 1 + d, 1+ 2d, ... , 1 + 100d from their mean is 255, then the d is equal to 

  • 10.0

  • 20.0

  • 10.1

  • 10.1

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6.

The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?

  • a = 0, b = 7 

  • a = 5, b = 2

  • a = 1, b = 6

  • a = 1, b = 6

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7.

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

  • 2log3e

  • loge3/2

  • log3e

  • log3e

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8.

If in a frequently distribution, the mean and median are 21 and 22 respectively, then its mode is approximately

  • 22.0

  • 20.5

  • 25.5

  • 25.5

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9.

In a series of 2n observations, half of them equal a and remaining half equal –a. If the standard deviation of the observations is 2, then |a| equals 

  • 1/n

  • square root of 2
  • 2

  • 2

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10.

Standard deviation of n observations a1, a2, a3, ... , an is 0. Then, the standard deviation of the observations λa1, λa2, ... , λan is

  • λσ

  • - λσ

  • λσ

  • λnσ


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