Question

1. the chess club at a school has 15 members. the number of games won this season by each member is listed. 1 2 3 3 4 5 5 5 6 8 8 10 11 16 24 30 a. below, find the 5 - number summary for this data. minimum q1 median q3 maximum b. create a box plot of the data. c. what measure of center is most appropriate to use for this data? mean or median. explain. d. calculate the iqr.

Explanation:

Step1: Arrange data in ascending order

2, 3, 3, 4, 5, 5, 5, 6, 8, 8, 10, 11, 16, 24, 30

Step2: Find the minimum

The minimum value is 2.

Step3: Find Q1 (first - quartile)

There are \(n = 15\) data points. The position of Q1 is \(\frac{n + 1}{4}=\frac{15+ 1}{4}=4\). So Q1 is the 4th value in the ordered - data set, which is 4.

Step4: Find the median

The position of the median is \(\frac{n + 1}{2}=\frac{15 + 1}{2}=8\). So the median is 6.

Step5: Find Q3 (third - quartile)

The position of Q3 is \(\frac{3(n + 1)}{4}=\frac{3\times(15 + 1)}{4}=12\). So Q3 is the 12th value in the ordered - data set, which is 11.

Step6: Find the maximum

The maximum value is 30.

Step7: Calculate the IQR

IQR=Q3 - Q1. So \(IQR = 11-4=7\)

Answer:

a. Minimum: 2, Q1: 4, Median: 6, Q3: 11, Maximum: 30
b. (To create a box - plot: Draw a number line that includes the range from 2 to 30. Draw a box from Q1 = 4 to Q3 = 11, draw a vertical line inside the box at the median 6. Draw whiskers from the box to the minimum 2 and maximum 30)
c. The median is more appropriate as the data seems to have some outliers (24 and 30). The mean can be affected by outliers, while the median is a more robust measure of central tendency in the presence of outliers.
d. IQR = 7