Question

algebra 1 unit 1: end - of - unit assessment
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.

Explanation:

Step1: Sort the data

First, sort the data set: 6, 6, 6, 7, 10, 11, 12, 13, 14, 14, 15, 16, 18, 18, 30.

Step2: Find the minimum

The smallest value in the sorted - data set is the minimum. So, the minimum is 6.

Step3: Find the first quartile (Q1)

The position of Q1 for a data set of size $n = 15$ is $i=\frac{n + 1}{4}=\frac{15+1}{4}=4$. So, Q1 is the 4th value in the sorted data set, which is 7.

Step4: Find the median

The position of the median for a data set of size $n = 15$ is $i=\frac{n + 1}{2}=\frac{15 + 1}{2}=8$. So, the median is the 8th value in the sorted data set, which is 13.

Step5: Find the third quartile (Q3)

The position of Q3 for a data set of size $n = 15$ is $i=\frac{3(n + 1)}{4}=\frac{3\times(15 + 1)}{4}=12$. So, Q3 is the 12th value in the sorted data set, which is 16.

Step6: Find the maximum

The largest value in the sorted - data set is the maximum. So, the maximum is 30.

Answer:

minimum	Q1	median	Q3	maximum