Q. 12 - The Practice of Statistics for AP

Question

You are interested in how much time students spend on the Internet each day. Here are data on the time spent on the Internet (in minutes) for a particular day reported by a random sample of 30 students at a large high school

(a) Construct a histogram of these data. (b) Are there any outliers? Justify your answer. (c) Would it be better to use the mean and standard deviation or the median and )12 to describe the center and spread of this distribution? Why? 

Step-by-Step Solution

Answer

a. The result of the numerical sequence is  

b. The difference between IQR is 47 and 151 is an outlier

c. The results are median and  IQR.

Step 1: Rearranging of numerical variables

Assume  rearrange all data in  sequence form of 7 to  151 data The data is seen as

Step 2: Result of difference of IQR

The average middle value is M = $Q_2=\left(\frac{46+47}{2}\right)= 46.5$

The first quartile  is 30

  the third is  77

 the difference between  third and fast is  47

Step 3: Equation of IQR

More than 1.5  times IQR on the survey  below Q1 and above Q3

$$\begin{gathered} Q_3+1.5IQR=77+\left(1.5\right)\times \left(47\right)=147.5 \\ {Q}_1+1.5IQR=30+\left(1.5\right)\times \left(47\right)=-40.5 \end{gathered}$$

As per solving the equation 151  is an outlier.

based on the 12a solution,  IQR and median are best as they are not affected by outliers but standard deviation and mean are also influenced by outliers. 

So, the results are median and  IQR.