Question

1. what is the five - number summary for the data 0, 2, 2, 4, 5, 5, 5, 5, 7, 11? minimum: 0 q1: 2 median: 5 q3: 5 maximum: 11 2. when the minimum, 0, is removed from the data set, what is the five - number summary? minimum: q1: median: q3: maximum: blank 1: 0 blank 2: 2 blank 3: 5 blank 4: 5 blank 5: 11

Explanation:

Step1: Organize the new data set

The new data - set after removing 0 is 2, 2, 4, 5, 5, 5, 5, 7, 11.

Step2: Find the minimum

The minimum value in the new data - set is 2.

Step3: Calculate the position of Q1

There are n = 9 data points. The position of Q1 is $\frac{n + 1}{4}=\frac{9+1}{4}=2.5$. So, Q1 is the average of the 2nd and 3rd ordered values. Q1=$\frac{2 + 4}{2}=3$.

Step4: Calculate the median

The position of the median for n = 9 data points is $\frac{n + 1}{2}=\frac{9+1}{2}=5$. The median is the 5th ordered value, which is 5.

Step5: Calculate the position of Q3

The position of Q3 is $\frac{3(n + 1)}{4}=\frac{3\times(9 + 1)}{4}=7.5$. So, Q3 is the average of the 7th and 8th ordered values. Q3=$\frac{5+7}{2}=6$.

Step6: Find the maximum

The maximum value in the new data - set is 11.

Answer:

Minimum: 2
Q1: 3
Median: 5
Q3: 6
Maximum: 11