Chapter 1.3, Problem 89E

(a)

To determine

To calculate the median of the given data.

Answer to Problem 89E

Median = 85

Explanation of Solution

Given:

The Dataset:

86	84	91	75	78	80	74
87	76	96	82	90	98	93

Formula used:

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

Calculation:

  $\begin{array}{l}\text{Median = }\frac{{\left(\frac{n}{2}\right)}^{\text{Th term}}+{\left(\frac{n}{2}+1\right)}^{\text{Th term}}}{2}\\ =\frac{{\left(\frac{14}{2}\right)}^{\text{Th term}}+{\left(\frac{14}{2}+1\right)}^{\text{Th term}}}{2}\\ =\frac{7^{\text{Th term}}+8^{\text{Th term}}}{2}\\ =\frac{84+86}{2}\\ =85\end{array}$

(b)

To determine

To explain the reason due to which 0 has no effect on the Median.

Explanation of Solution

The median is a measure of central tendency which is resistant to the outlier values. Which means it does not have any affect due to the extreme values. Median lies in the middle of the data and it does not involve each observation into the account while calculating.