Olympiad – Class X – Mathematics - Statistics

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Question - 1

Find the weighted mean of first 'n' natural numbers, whose weights are proportional to the corresponding numbers.

  • A \(\frac{2n+1}{3}\)
  • B \(\frac{n+1}{2}\)
  • C \(\frac{n(n+1)}{2}\)
  • D \(\frac{(n+1)(2n+1)}{2}\)

Question - 2

What is the mean of - 8, -4, 4 and 8?

  • A 1
  • B zero
  • C 8
  • D 2

Question - 3

Find the mean of the first six multiples of 3.

  • A 63
  • B 11.5
  • C 10.5
  • D 60

Question - 4

The A.M. of a set of 50 numbers is 38. If two numbers of the set, namely 55 and 45 are discarded, find the mean of the remaining observations.

  • A 36
  • B 37.5
  • C 36.5
  • D 38.5

Question - 5

Find the mean of the first six prime numbers.

  • A 68.3
  • B 6.71
  • C 7
  • D 6.83

Question - 6

The A.M. of 'n' numbers of a series is \(\overline { X } \) . If the sum of first (n - 1) terms is 'k', what is the nth number?

  • A n\(\overline { X } \)-nk
  • B n\(\overline { X } \)-k
  • C \(\overline { X } \)-nk
  • D \(\overline { X } \)-k

Question - 7

The mean age of a combined group of men and women is 25 years. If the mean age of the group of men is 26 years and that of the group of women is 21 years, find the percentage of men and women respectively in the group.

  • A 70,30
  • B 30,70
  • C 80,20
  • D 60,40

Question - 8

The mean of 8 numbers is 25. If 5 is subtracted from each number, what will the new mean be?

  • A 20
  • B 15
  • C 160
  • D 2

Question - 9

If the mean of first 'n' odd natural numbers is 'n' itself,what is the value of 'n'?

  • A 2
  • B 3
  • C 1
  • D Any natural number

Question - 10

If the mean of 'n' observations, 12, 22, 32,....,n2 is \(\frac{46n}{11}\) find the value of 'n'.

  • A 22
  • B 23
  • C 12
  • D 11
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