Question

answer the statistical measures and create a box and whiskers plot for the following set of data. enter all values as whole numbers or decimals. 3,3,4,5,5,5,8,9,10,10,11,11,15,15 min: q1: med: q3: max: create the box plot by dragging the lines: box plot with number line from 0 to 20

Explanation:

Step1: Find Minimum (Min)

The minimum value is the smallest number in the data set.
Looking at the data: \( 3, 3, 4, 5, 5, 5, 8, 9, 10, 10, 11, 11, 15, 15 \), the smallest number is \( 3 \).

Step2: Find Median (Med)

The median is the middle value of a sorted data set. Since there are \( n = 14 \) (even) values, the median is the average of the \( \frac{n}{2} = 7 \)-th and \( \frac{n}{2}+1 = 8 \)-th values.
Sorted data: positions 1 - 14: \( 3, 3, 4, 5, 5, 5, 8, 9, 10, 10, 11, 11, 15, 15 \)
7th value: \( 8 \), 8th value: \( 9 \)
Median \( = \frac{8 + 9}{2} = 8.5 \)

Step3: Find First Quartile (Q1)

Q1 is the median of the lower half of the data. The lower half is the first \( \frac{n}{2}=7 \) values: \( 3, 3, 4, 5, 5, 5, 8 \)
There are 7 (odd) values, so the median of this subset is the 4th value.
4th value: \( 5 \), so \( Q1 = 5 \)

Step4: Find Third Quartile (Q3)

Q3 is the median of the upper half of the data. The upper half is the last \( \frac{n}{2}=7 \) values: \( 9, 10, 10, 11, 11, 15, 15 \)
There are 7 (odd) values, so the median of this subset is the 4th value.
4th value: \( 11 \), so \( Q3 = 11 \)

Step5: Find Maximum (Max)

The maximum value is the largest number in the data set.
Looking at the data, the largest number is \( 15 \).

Answer:

Min: \( 3 \)
Q1: \( 5 \)
Med: \( 8.5 \)
Q3: \( 11 \)
Max: \( 15 \)

For the box - and - whisker plot:

• The left whisker starts at the minimum value (\( 3 \)) and ends at \( Q1 \) (\( 5 \)).
• The box starts at \( Q1 \) (\( 5 \)), has a line at the median (\( 8.5 \)) and ends at \( Q3 \) (\( 11 \)).
• The right whisker starts at \( Q3 \) (\( 11 \)) and ends at the maximum value (\( 15 \)).