) The mean and median of five non zero natural numbers are 8 and 6 respectively. 15 is the only mode of these five non zero natural 3 numbers. What will be the range and the interquartile range of these five non zero natural numbers?

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The correct answer is: The range and the interquartile range of these five non zero natural numbers is 14 and 11 respectively.

Given: The mean and median of five non zero natural numbers are 8 and 6 respectively. 15 is the only mode of these five non zero natural 3 numbers.

To Find:

What will be the range and the interquartile range of these five non zero natural numbers?

Solution:

To find the range, we need to find the difference between the largest and smallest number in the set. Since 15 is the only mode, it must be one of the numbers in the set. Since the mean of the set is 8, the sum of the five numbers must be 40 (8 x 5).

Let's assume that the five numbers are a, b, c, d, and 15 (since 15 is the only mode).

We know that:

a + b + c + d + 15 = 40

a + b + c + d = 25

Since the median is 6, either c or d must be 6. Let's assume that c = 6.

We also know that:

(a + b + d)/3 = 8

a + b + d = 24

Now we have two equations with two variables:

a + b + d = 24

a + b + 6 = 19

Subtracting the second equation from the first, we get:

d - 6 = 5

d = 11

Substituting d = 11 into the equation a + b + d = 24, we get:

a + b = 13

Since a, b, and d are all different non-zero natural numbers, they must be 1, 2, and 11 (in some order).

Therefore, the set of five non-zero natural numbers is {1, 2, 6, 11, 15}.

The range is the difference between the largest and smallest number in the set:

The range is the difference between the largest and smallest number in the set: Range = 15 - 1 = 14

To find the interquartile range, we need to find the difference between the third quartile (Q3) and the first quartile (Q1).

Since there are only five numbers in the set, Q2 (the median) is the middle number (6). Q1 is the median of the lower half of the set ({1, 2, 6}), which is 2. Q3 is the median of the upper half of the set ({11, 15}), which is 13.

Therefore,

Therefore,Interquartile range = Q3 - Q1 = 13 - 2 = 11

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