Question

there is a group of 8 kids. what is their median age? 3, 17, 17, 11, 8, 13, 5, 18
13
12
17
11
question 6
2 pts
a high school football team has a good defense. during there 9 - game season, they gave up the following amount of points: 7, 20, 34, 7, 16, 8, 10, 7, 17
given that above set of numbers,
the mean is
the mode is
the median is
the range is

Explanation:

Step1: Arrange data in ascending order

For the first - part data of kids' ages: 3, 5, 8, 11, 13, 17, 17, 18. Since there are $n = 8$ (an even number of data points), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+ 1)$th ordered values. $\frac{n}{2}=\frac{8}{2}=4$ and $\frac{n}{2}+1 = 5$. The 4th value is 11 and the 5th value is 13.
Median $=\frac{11 + 13}{2}=\frac{24}{2}=12$.

Step2: For the football - team data

Arrange the points data in ascending order: 7, 7, 7, 8, 10, 16, 17, 20, 34.

Mean calculation

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 9$ and $\sum_{i=1}^{9}x_{i}=7+7+7+8+10+16+17+20+34 = 126$. So, $\bar{x}=\frac{126}{9}=14$.

Mode calculation

The mode is the value that appears most frequently. Here, 7 appears 3 times, more frequently than any other number, so the mode is 7.

Median calculation

Since $n = 9$ (an odd number of data points), the median is the $(\frac{n + 1}{2})$th value. $\frac{n+1}{2}=\frac{9 + 1}{2}=5$th value. The 5th value in the ordered list is 10, so the median is 10.

Range calculation

The range is the difference between the maximum and minimum values. Range $=34 - 7=27$.

Answer:

For the first question: B. 12
For the second question:
The Mean is 14
The Mode is 7
The Median is 10
The Range is 27