Question

the king high school football team has three players who take turns playing running back. the coach records the number of yards the players gain on each carry. here are the results for the most recent game. neil 5 0 8 4 3 6 5 1 2 7 4 jaden 8 11 19 0 0 2 6 8 11 1 5 darnel 0 12 3 7 4 6 2 7 4 5 7 based on the data, which statement is not true? the lower quartile of neils carries is less than the lower quartile of jadens carries. the median of darnels carries is less than the upper quartile of jadens carries. the upper quartile of neils carries is equal to the median of jadens carries. the interquartile range of neils carries is equal to the interquartile range of darnels carries.

Explanation:

Step1: Arrange Neil's data in ascending order

0, 1, 2, 3, 4, 4, 5, 5, 6, 7, 8
There are $n = 11$ data - points. The lower - quartile ($Q_1$) position is $\frac{n + 1}{4}=\frac{11+1}{4}=3$. So, $Q_1 = 2$. The upper - quartile ($Q_3$) position is $\frac{3(n + 1)}{4}=\frac{3\times(11 + 1)}{4}=9$. So, $Q_3 = 6$. The inter - quartile range (IQR) is $Q_3−Q_1=6 - 2=4$.

Step2: Arrange Jaden's data in ascending order

0, 0, 1, 2, 5, 6, 8, 8, 11, 11, 19
There are $n = 11$ data - points. The lower - quartile position is $\frac{n + 1}{4}=3$. So, $Q_1 = 1$. The upper - quartile position is $\frac{3(n + 1)}{4}=9$. So, $Q_3 = 11$. The median position is $\frac{n + 1}{2}=6$, and the median is 6.

Step3: Arrange Darnel's data in ascending order

0, 2, 3, 4, 4, 5, 6, 7, 7, 7, 12
There are $n = 11$ data - points. The median position is $\frac{n+1}{2}=6$. So, the median is 5. The lower - quartile position is $\frac{n + 1}{4}=3$. So, $Q_1 = 3$. The upper - quartile position is $\frac{3(n + 1)}{4}=9$. So, $Q_3 = 7$. The IQR is $Q_3−Q_1=7 - 3=4$.

Step4: Check each statement

• For the first statement: Neil's $Q_1 = 2$ and Jaden's $Q_1 = 1$. Since $2>1$, the statement "The lower quartile of Neil's carries is less than the lower quartile of Jaden's carries" is not true.
• For the second statement: Darnel's median is 5 and Jaden's $Q_3$ is 11. Since $5<11$, the statement "The median of Darnel's carries is less than the upper quartile of Jaden's carries" is true.
• For the third statement: Neil's $Q_3 = 6$ and Jaden's median is 6. So, the statement "The upper quartile of Neil's carries is equal to the median of Jaden's carries" is true.
• For the fourth statement: Neil's IQR is 4 and Darnel's IQR is 4. So, the statement "The interquartile range of Neil's carries is equal to the interquartile range of Darnel's carries" is true.

Answer:

The lower quartile of Neil's carries is less than the lower quartile of Jaden's carries.