Question

1. the box plots below summarize the ages of athletes on the swim team and the track team. swim team track team 9 10 11 12 13 14 15 16 17 8 9 10 11 12 13 14 15 based on the box plots, which statement must be true? (1) the iqr of both teams is the same. (2) there are more athletes on the swim team than on the track team. (3) the median age of the swim team is less than the median age of the track team. (4) the range of ages of the swim team is smaller than the range of ages of the track team. 5. a class of 20 students was surveyed to determine the number of pets each student owned. the data are represented in the dot - plot below. which statement about the data is correct? (1) the mean and the median are the same. (2) the median and the mode are the same. (3) the mean and the mode are the same. (4) the mean, median, and mode are all the same

Explanation:

Question 4

Step1: Recall IQR formula

$IQR = Q_3 - Q_1$ (where $Q_3$ is the third - quartile and $Q_1$ is the first - quartile). For the swim team, $Q_1 = 13$, $Q_3=15$, so $IQR_{swim}=15 - 13=2$. For the track team, $Q_1 = 10$, $Q_3 = 12$, so $IQR_{track}=12 - 10 = 2$.

Step2: Analyze other statements

• The number of athletes cannot be determined from box - plots.
• The median of the swim team is around 14 and the median of the track team is around 11, so the median of the swim team is greater.
• The range of the swim team is $17 - 9=8$ and the range of the track team is $15 - 8 = 7$, so the range of the swim team is larger.

Step1: Find the mode

The mode is the most frequently occurring value. From the dot - plot, the mode is 2 (since there are 7 dots above 2).

Step2: Find the median

There are $n = 20$ data points. The median is the average of the 10th and 11th ordered data points. Counting the dots, the 10th and 11th values are both 2. So the median is 2.

Step3: Find the mean

$\bar{x}=\frac{0\times1 + 1\times5+2\times7 + 3\times4+4\times2+5\times1}{20}=\frac{0 + 5+14 + 12+8+5}{20}=\frac{44}{20}=2.2$

Answer:

(1) The IQR of both teams is the same.

Question 5