Question

algebra 1 unit 1: end - of - unit assessment
directions: show all your work. you may use a calculator.

1. the chess club at a school has 15 members. the number of games won in tournament play this season by each member is listed. use this data to answer all of the questions on this page.

6 6 6 7 10 11 12 13 14 14 15 16 18 18 30
a. create a five - number summary for this data.

minimum

q1

median

q3

maximum

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b. draw the box plot for this data.
6 7 10 11 12 13 14 15 16 18 30
0 4 8 12 16 20 24 28 32
games won
c. calculate the interquartile range for this data set.
d. is the number 30 an outlier in this data set? show or explain your reasoning.

Explanation:

Step1: Find the minimum

The minimum value in the data - set {6, 6, 6, 7, 10, 11, 12, 13, 14, 14, 15, 16, 18, 18, 30} is 6.

Step2: Find the first quartile (Q1)

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 - ordered value, which is 7.

Step3: Find the median

The position of the median for \(n = 15\) (an odd - numbered data set) is \(\frac{n + 1}{2}=\frac{15 + 1}{2}=8\). So, the median is 13.

Step4: Find the third quartile (Q3)

The position of Q3 is \(3\times\frac{n + 1}{4}=3\times\frac{15 + 1}{4}=12\). So, Q3 is the 12th - ordered value, which is 16.

Step5: Find the maximum

The maximum value in the data - set is 30.

Step6: Calculate the inter - quartile range (IQR)

\(IQR=Q3 - Q1=16 - 7 = 9\).

Step7: Check for outliers

The lower fence for outliers is \(Q1-1.5\times IQR=7-1.5\times9=7 - 13.5=-6.5\). The upper fence for outliers is \(Q3 + 1.5\times IQR=16+1.5\times9=16 + 13.5=29.5\). Since \(30>29.5\), 30 is an outlier.

Answer:

a.

minimum	Q1	median	Q3	maximum

c. \(IQR = 9\)
d. Yes, 30 is an outlier because it is greater than the upper - fence of \(29.5\) (where the upper - fence is calculated as \(Q3+1.5\times IQR\) with \(Q3 = 16\) and \(IQR = 9\)).