Chapter 2, Problem R2.3RE

(a)

To determine

To find: the mean, median, standard deviation and IQR for the transformed data.

Answer to Problem R2.3RE

  $\begin{array}{l}\overline{x}=13.3232\\ Median=12.8049\\ s=3.8110\\ IQR=2.5915\end{array}$

Explanation of Solution

Given:

  

  $\begin{array}{c}\overline{x}=43.70\\ MEDIN=42.00\\ s=12.50\\ Q_1=35.50\\ Q_3=44.00\end{array}$

Calculation:

Relationship between feet and meter:

  $3.2ft=1m\Rightarrow 1ft=\frac{1}{3.28}m$

The inter quartile range is the difference between the third and the first quartile:

  $\begin{array}{c}IQR=Q_3-Q_1\\ =44.00-35.50\\ =8.50\end{array}$

Divide by 3.28 to convert the measurement from feet to meter:

  $\begin{array}{c}\overline{x}=\frac{43.70}{3.28}=13.3232\\ MEDIAN=\frac{42.00}{3.28}=12.8049\\ s=\frac{12.50}{3.28}=3.8110\\ IQR=\frac{8.50}{3.28}=2.5915\end{array}$

The shape of the distribution would not be affected because the every data value is converted in the same manner and therefore the data values would remain distributed in the same manner

(b)

To determine

To find: the mean and standard deviation of the errors in feet.

Answer to Problem R2.3RE

  $\begin{array}{c}\overline{x}=1.1\\ s=12.50\end{array}$

Explanation of Solution

Given:

  

Data of the width of their classroom in feet:

  $\begin{array}{c}\overline{x}=43.70\\ s=12.50\end{array}$

Calculation:

The distribution of the errors is every guess decreased by 42. 6. Then mean than decreases by the same amount:

  $\overline{x}=43.70-42.60=1.1$

The standard deviation would remain not affected because the spread would not be changed when every value decreased by the same amount

  $s=12.50$

(c)

To determine

To find: the percentile for the student who calculated the class room width as 63 feet.

Answer to Problem R2.3RE

92^nd percentile

Explanation of Solution

Given:

  

  $n=\text{sample size =66}$

Calculation:

The summary statistic is having 66 below n, which shows that the data set is having 66 data values.

It is observed that in the dot plot, that 4 dots are to the right of 63 and 1 dot associates with 63, which means that 66 - 4 - 1 = 61 dots of the 66 dots are to the left of 63.

Required percentile

  $\begin{array}{c}\text{Percentile=}\frac{\text{Number of data values that are less than the individual's data value}}{\text{Total number of data values}}\times 100\%\\ =\frac{61}{66}\times 100\%\\ =0.92\times 100\%\\ =92\%\end{array}$

Therefore the percentile associating with 63 feet is the 92^nd percentile.