Chapter 6.A, Problem 1QQ

To determine

The method of determining the median weight of 51 pumpkin

Answer to Problem 1QQ

Solution:

Arrange the weight of pumpkin in increasing order and find out the weight of pumpkin present in the middle.

Explanation of Solution

Given:

Weight of 51 pumpkin

Formula Used:

Let n be the number of terms in the series in increasing order

Case I:

If n is odd

$Median={\left(\frac{n+1}{2}\right)}^{\text{th}}\text{term}$

Case II:

If n is even

$Median=\frac{{\left(\frac{n}{2}\right)}^{\text{th}}\text{term+}{\left(\frac{n}{2}+1\right)}^{\text{th}}\text{term}}{2}$

Calculation:

Here, we have the weights of 51 pumpkin which are arranged in increasing order. As here n = 51, an odd value.

Thus, the median weight of given pumpkin is

$\text{Median}\text{weight}={\left(\frac{51+1}{2}\right)}^{\text{th}}{\text{term = Weight of 26}}^{\text{th}}\text{pumpkin}$

For example, a series is given 9, 7, 6, 10, 12, 3, 5. Then arrangement of series is done in increasing order and it becomes 3, 5, 6, 7, 9, 10, 12.

Now, 7 is the middle value and thus is required the median of the series.

Conclusion:

Hence, after arranging the weight of pumpkin in increasing order, the weight of pumpkin present in the middle is the median weight of the pumpkin.