Question

the number of pages read by two students each day for 5 days are listed in the table.

student	number of pages in each book
aaron	55, 19, 40, 16, 75

which statements are true regarding the two data sets? check all that apply.

• the means for both data sets are equal.
• the means for the data sets are not equal.
• the range of the number of pages lionel read is greater than the range of the number of pages aaron read.
• the range of the number of pages that lionel read is 75.
• the range of the number of pages that aaron read is 50.

Explanation:

Step1: Calculate the mean for Lionel

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. For Lionel, $n = 5$, $x_{1}=90,x_{2}=45,x_{3}=30,x_{4}=25,x_{5}=15$.
$\sum_{i=1}^{5}x_{i}=90 + 45+30 + 25+15=205$.
$\bar{x}_{L}=\frac{205}{5}=41$.

Step2: Calculate the mean for Aaron

For Aaron, $n = 5$, $x_{1}=55,x_{2}=19,x_{3}=40,x_{4}=16,x_{5}=75$.
$\sum_{i = 1}^{5}x_{i}=55+19 + 40+16+75=205$.
$\bar{x}_{A}=\frac{205}{5}=41$.

Step3: Calculate the range for Lionel

The range formula is $R=\text{Max}-\text{Min}$. For Lionel, $\text{Max}=90$, $\text{Min}=15$.
$R_{L}=90 - 15=75$.

Step4: Calculate the range for Aaron

For Aaron, $\text{Max}=75$, $\text{Min}=16$.
$R_{A}=75 - 16=59$.

Answer:

• The means for both data sets are equal.
• The range of the number of pages that Lionel read is 75.