Question

1. use the data set to calculate the measures of center below: 5, 18, 5, 15, 7, 12, 8, 10

mode=
range=
mean=
median=

Explanation:

Step1: Sort the data set

First, we sort the data set \( 5, 18, 5, 15, 7, 12, 8, 10 \) in ascending order. The sorted data set is \( 5, 5, 7, 8, 10, 12, 15, 18 \).

Step2: Calculate the range

The range is calculated as the difference between the maximum value and the minimum value in the data set. The maximum value is \( 18 \) and the minimum value is \( 5 \). So, the range is \( 18 - 5 = 13 \).

Step3: Calculate the mean

The mean is the sum of all values divided by the number of values. The sum of the values is \( 5 + 5 + 7 + 8 + 10 + 12 + 15 + 18 \). Let's calculate the sum: \( 5+5 = 10 \), \( 10 + 7 = 17 \), \( 17 + 8 = 25 \), \( 25 + 10 = 35 \), \( 35 + 12 = 47 \), \( 47 + 15 = 62 \), \( 62 + 18 = 80 \). There are \( 8 \) values. So, the mean is \( \frac{80}{8} = 10 \).

Step4: Verify the median (already partially done)

The median of a data set with an even number of values is the average of the two middle numbers. The sorted data set has \( 8 \) values, so the two middle numbers are the \( 4^{th} \) and \( 5^{th} \) values, which are \( 8 \) and \( 10 \). The median is \( \frac{8 + 10}{2} = 9 \) (which matches the given median, so we can confirm this step).

Step5: Confirm the mode (already partially done)

The mode is the value that appears most frequently. In the data set, \( 5 \) appears twice, and all other values appear once. So, the mode is \( 5 \).

Answer:

• Mode: \( 5 \)
• Range: \( 13 \)
• Mean: \( 10 \)
• Median: \( 9 \)