Chapter 1.3, Problem 90E

(a)

To determine

To calculate the median of the given data.

Answer to Problem 90E

Median = 76

Explanation of Solution

Given:

The Dataset:

71	104	76	88	78	71	68	86	70	90
74	76	69	68	88	96	68	82	120

Formula used:

  $\text{Median = }\left\{\begin{array}{l}\frac{{\left(\frac{n}{2}\right)}^{\text{Th term}}+{\left(\frac{n}{2}+1\right)}^{\text{Th term}}}{2},\text{ When n is even }\\ {\left(\frac{n+1}{2}\right)}^{\text{Th term}},\text{ When n is odd}\end{array}\right\}$

Calculation:

  $\begin{array}{l}\text{Median = }{\left(\frac{n+1}{2}\right)}^{\text{Th term}}\\ ={\left(\frac{19+1}{2}\right)}^{\text{Th term}}\\ ={10}^{\text{Th term}}\\ =76\end{array}$

(b)

To determine

To calculate the median after removing the value 120 and explain the reason due to which removing120 has no effect on the Median.

Answer to Problem 90E

Median = 76

Explanation of Solution

Calculation:

  $\begin{array}{l}\text{Median = }\frac{{\left(\frac{n}{2}\right)}^{\text{Th term}}+{\left(\frac{n}{2}+1\right)}^{\text{Th term}}}{2}\\ =\frac{{\left(\frac{18}{2}\right)}^{\text{Th term}}+{\left(\frac{18}{2}+1\right)}^{\text{Th term}}}{2}\\ =\frac{9^{\text{Th term}}+{10}^{\text{Th term}}}{2}\\ =\frac{76+76}{2}\\ =76\end{array}$

The median is a measure of central tendency which is resistant to the outlier values and the extreme 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. Here, 120 is the extreme value which comes due to the medical issues or the confounding variable.