Chapter 1.3, Problem 90E

(a)

To determine

To find: theflier interquartile range (IQR).

Answer to Problem 90E

The flier interquartile range is 12

Explanation of Solution

Given:

S No	Quiz grades
1	285
2	303
3	305
4	306
5	309
6	315
7	318

Calculation:

The flier interquartile range (IQR) is calculated as

  $\begin{array}{l}{Q}_1=\frac{N+1}{4}\text{th}\text{item}\\ Q_1=\frac{7+1}{4}\text{th}\text{item}\\ Q_1=\frac{8}{4}\text{th}\text{item}\\ Q_1=2\text{nd}\text{item=303}\end{array}$

  $\begin{array}{l}{Q}_3=\frac{3\left(N+1\right)}{4}\text{th}\text{item}\\ Q_3=\frac{3\left(7+1\right)}{4}\text{th}\text{item}\\ Q_3=\frac{24}{4}\text{th}\text{item}\\ Q_3=6\text{th}\text{item=315}\end{array}$

  $\begin{array}{l}IQR=Q_3-Q_1\\ =315-303\\ =12\end{array}$

Conclusion:

Therefore, the flier interquartile range is 12

(b)

To determine

whether there are any outliers

Answer to Problem 90E

All the items are within the range thus there are no outliers.

Explanation of Solution

From Joe's first 14 quiz grades in a marking period data we can say that there are no outliers in the data. We call an observation as an outlier if it falls more than $1.5\times IQR$ above the third quartile or below the first quartile

  $\begin{array}{l}IQR\times 1.5\\ 12\times 1.5=18\\ Q_1-18=303-18\\ =285\\ Q_3-18=315+18\\ =333\end{array}$

All the items are within the range thus there are no outliers.

Conclusion:

Thus there are no outliers.