Question

the bar graph shows the number of games a soccer team played each month. use the data to find each measure. median = range = interquartile range = which is true of this data? the values are clustered around the median. the values are spread out. the data shows a lot of variability. the data shows a large spread

Explanation:

Step1: List the data values

The number of games per month are 7 (Jan), 5 (Feb), 3 (Mar), 8 (Apr), 6 (May).

Step2: Find the median

Arrange the data in ascending - order: 3, 5, 6, 7, 8. Since there are 5 values (an odd number), the median is the middle value. So, the median is 6.

Step3: Find the range

The range is the difference between the maximum and minimum values. The maximum value is 8 and the minimum value is 3. Range = 8 - 3=5.

Step4: Find the inter - quartile range

First, find the first quartile ($Q_1$) and the third quartile ($Q_3$). The lower half of the data is 3, 5. The median of the lower half ($Q_1$) is $\frac{3 + 5}{2}=4$. The upper half of the data is 7, 8. The median of the upper half ($Q_3$) is $\frac{7+8}{2}=7.5$. The inter - quartile range (IQR) is $Q_3−Q_1=7.5 - 4 = 3.5$.

Step5: Analyze the data

The values are 3, 5, 6, 7, 8. They are spread out as the range is 5 and the IQR is 3.5.

Answer:

Median = 6
Range = 5
Interquartile range = 3.5
The values are spread out.