Question

Find the median of the squares of the first 8 natural numbers

Answer 1

1 square=1

2 square=4

3 square=9

4 square=16

5 square=25

6 square=36

7 square=49

8 square=64

1,4,9,16,25,36,49,64

by cancelling from the ends, the numbers left over are 16, 25

so add them and divide by 2 and the answer will be 16+25/2= 20.5

therefore, 20.5 is the median of the squares of the first 8 natural numbers.

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Answer 2

Answer:

Median of the squares of the first 8 natural numbers i.e.

{ 1,4,9,16,25,36,49,64}  is 20.5

Step-by-step explanation:

• First 8 natural numbers are 1,2,3,4,5,6,7,8
• Squares of the first 8 natural numbers: 1,4,9,16,25,36,49,64

• Median is the value of the middle-most observation that can be obtained by arranging the data in ascending order .
• Median is the value at the mid-point of the dataset, not the mid-point of the values.
• For the even number of observations, there are two middle position.

Median can be calculated by the following way:

Step 1: Arrange the data items in ascending order.

          Ordered Set: { 1,4,9,16,25,36,49,64}

Step 2: Count the number of observations.

           Number of observations n = 8 (even)

Step 3:  Median =[ $\frac{n}{2}$th observation + ( $\frac{n}{2}$+ 1) th observation ]/ 2

  Hence Median = [4tn observation + 5th observation] / 2

                            =( 16+25 ) / 2 = 41/2 = 20.5

So, median of the squares of the first 8 natural numbers is 20.5