Question

question 5 (2 points)

1. what is the five - number summary for the data 0, 2, 2, 4, 5, 5, 5, 5, 7, 11?

minimum:
q1:
median:
q3:
maximum:

1. when the minimum, 0, is removed from the data set, what is the five - number summary?

minimum:
q1:
median:
q3:
maximum:

blank 1:
blank 2:
blank 3:
blank 4:
blank 5:
blank 6:

Explanation:

Step1: Arrange data in ascending order for first - part

The data set is \(0,2,2,4,5,5,5,5,7,11\).

Step2: Find minimum for first - part

The minimum value is \(0\).

Step3: Calculate position of Q1 for first - part

There are \(n = 10\) data points. The position of \(Q1\) is \(i=\frac{n + 1}{4}=\frac{10+1}{4}=2.75\). So \(Q1=2+(0.75)\times(4 - 2)=2 + 1.5 = 2\).

Step4: Calculate position of median for first - part

The position of the median is \(i=\frac{n+1}{2}=\frac{10 + 1}{2}=5.5\). So the median is \(\frac{5+5}{2}=5\).

Step5: Calculate position of Q3 for first - part

The position of \(Q3\) is \(i=\frac{3(n + 1)}{4}=\frac{3\times(10 + 1)}{4}=8.25\). So \(Q3=5+(0.25)\times(7 - 5)=5+0.5 = 5\).

Step6: Find maximum for first - part

The maximum value is \(11\).

Step7: Arrange data in ascending order for second - part

After removing \(0\), the data set is \(2,2,4,5,5,5,5,7,11\). There are \(n = 9\) data points.

Step8: Find minimum for second - part

The minimum value is \(2\).

Step9: Calculate position of Q1 for second - part

The position of \(Q1\) is \(i=\frac{n + 1}{4}=\frac{9+1}{4}=2.5\). So \(Q1=\frac{2 + 4}{2}=3\).

Step10: Calculate position of median for second - part

The position of the median is \(i=\frac{n+1}{2}=\frac{9 + 1}{2}=5\). So the median is \(5\).

Step11: Calculate position of Q3 for second - part

The position of \(Q3\) is \(i=\frac{3(n + 1)}{4}=\frac{3\times(9 + 1)}{4}=7.5\). So \(Q3=\frac{5+7}{2}=6\).

Step12: Find maximum for second - part

The maximum value is \(11\).

Answer:

1. Minimum: \(0\)

Q1: \(2\)
Median: \(5\)
Q3: \(5\)
Maximum: \(11\)

1. Minimum: \(2\)

Q1: \(3\)
Median: \(5\)
Q3: \(6\)
Maximum: \(11\)