Question

question
answer the statistical measures and create a box and whiskers plot for the following set of data.
7, 9, 9, 11, 12, 14, 15, 18
enter all values as whole numbers or decimals.
min:
q1:
med:
q3:
max:
create the box plot by dragging the lines:

Explanation:

Step1: Identify Min and Max

The data set is \( 7, 9, 9, 11, 12, 14, 15, 18 \). The minimum value (Min) is the smallest number, and the maximum value (Max) is the largest number.
Min: \( 7 \)
Max: \( 18 \)

Step2: Find the Median (Med)

First, the data is already ordered. Since there are 8 data points (even number), the median is the average of the 4th and 5th values.
4th value: \( 11 \), 5th value: \( 12 \)
Med: \( \frac{11 + 12}{2} = 11.5 \)

Step3: Find Q1 (First Quartile)

Q1 is the median of the lower half of the data. The lower half is \( 7, 9, 9, 11 \) (first 4 values). The median of these 4 values (even number) is the average of the 2nd and 3rd values.
2nd value: \( 9 \), 3rd value: \( 9 \)
Q1: \( \frac{9 + 9}{2} = 9 \)

Step4: Find Q3 (Third Quartile)

Q3 is the median of the upper half of the data. The upper half is \( 12, 14, 15, 18 \) (last 4 values). The median of these 4 values (even number) is the average of the 2nd and 3rd values.
2nd value: \( 14 \), 3rd value: \( 15 \)
Q3: \( \frac{14 + 15}{2} = 14.5 \)

Answer:

Min: \( 7 \)
Q1: \( 9 \)
Med: \( 11.5 \)
Q3: \( 14.5 \)
Max: \( 18 \)

For the box - plot:

• The left whisker extends from Min (\( 7 \)) to Q1 (\( 9 \)).
• The box is between Q1 (\( 9 \)) and Q3 (\( 14.5 \)), with a line inside the box at the median (\( 11.5 \)).
• The right whisker extends from Q3 (\( 14.5 \)) to Max (\( 18 \)).