For the set of numbers x, x, x + 2, x + 3, x + 10 where x is a natural number, which of the following is/are correct? (1) Mean > Mode (2) Median > Mean

By Raj Vimal|Updated : September 27th, 2022

Select the correct answer using the code given below.

(A) 1 only

(B) 2 only

(C) Both 1 and 2

(D) Neither 1 nor 2

For the set of numbers x, x, x + 2, x + 3, x + 10 where x is a natural number Mean > Mode is correct. The ratio between the total number of observations and the sum of all observations is known as the mean.

Why is Mean > Mode correct?

The value that repeatedly appears in a given set is the mode. The mean, mode, and median are related: Mode = 3(Median) - 2(Mean).

Given a set of numbers are x, x, x + 2, x + 3, x + 10.

According to the question, x is a natural number, then put x = 1

The set of numbers are

1, 1, 3, 4, 11.

  • Mean = 1 + 1 + 3 + 4 + 11/5
  • Mean = 3
  • Mode = 1
  • Mean > Mode

Therefore, statement 1 is correct.

We know that Mode = 3 (Median) - 2 (Mean)

  • 1 = 3(Median) - 2(4)
  • 3(Median) = 9
  • Median = 3
  • Median < Mean
  • Therefore, statement 2 is incorrect

Summary:

For the set of numbers x, x, x + 2, x + 3, x + 10 where x is a natural number, which of the following is/are correct? (1) Mean > Mode (2) Median > Mean.

For the set of numbers x, x, x + 2, x + 3, and x + 10, Mean > Mode is correct. Here x is a natural number. To find this statement correct, suppose X is equal to 1.

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