Question

the 9th - grade track team is getting ready for their first big race. over one week, coach smith recorded the number of laps each team member ran during practice. the team has 20 students. here is the number of laps each student ran in one practice session: 7, 8, 10, 12, 7, 9, 13, 15, 12, 10, 8, 14, 11, 13, 9, 10, 12, 13, 11, 8
group frequency mean: 7 - 8 9 - 10 median: 11 - 12 13 - 15 mode:

Explanation:

Step1: Calculate frequencies

Count the number of data - points in each group.
For the group 7 - 8: There are 6 values (7, 8, 7, 8, 8, 8), so the frequency is 6.
For the group 9 - 10: There are 7 values (9, 10, 9, 10, 10, 9, 10), so the frequency is 7.
For the group 11 - 12: There are 5 values (12, 12, 12, 11, 11), so the frequency is 5.
For the group 13 - 15: There are 2 values (13, 15, 13, 13), so the frequency is 4.

Step2: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$.
$\sum_{i=1}^{20}x_{i}=7\times2 + 8\times4+9\times3 + 10\times4+11\times2+12\times4+13\times3+15\times1$
$=14 + 32+27 + 40+22+48+39+15$
$=237$.
$n = 20$, so $\bar{x}=\frac{237}{20}=11.85$.

Step3: Calculate the median

Since $n = 20$ (an even number), the median is the average of the $\frac{n}{2}=10$th and $(\frac{n}{2}+1)=11$th ordered values.
First, order the data: 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 12, 12, 12, 13, 13, 13, 15.
The 10th value is 10 and the 11th value is 10, so the median is $\frac{10 + 10}{2}=10$.

Step4: Calculate the mode

The mode is the value that appears most frequently. The value 10 appears 4 times, 8 appears 4 times, and 12 appears 4 times and 13 appears 3 times. So the modes are 8, 10, 12.

The completed table:

Group	Frequency
9 - 10	7
11 - 12	5
13 - 15	4

Mean: 11.85
Median: 10
Mode: 8, 10, 12

Answer:

Group	Frequency
9 - 10	7
11 - 12	5
13 - 15	4

Mean: 11.85
Median: 10
Mode: 8, 10, 12