Answer the statistical measures and create a box and whiskers plot for the following set of data., On this question page, you will first be asked to fill in statistical measures, then create a box plot. Once you make adjustments to the box plot, the answer area will appear and you will be able to submit your answers.

Question

6, comma, 7, comma, 8, comma, 9, comma, 9, comma, 10, comma, 10, comma, 10, comma, 11, comma, 11, comma, 12, comma, 13, comma, 14, comma, 15, comma, 15
6,7,8,9,9,10,10,10,11,11,12,13,14,15,15
Min:
Q1:
Med:
Q3:
Max:
Create the box plot by dragging the lines:

Answer 1

To properly summarize the provided data set (6, 7, 8, 9, 9, 10, 10, 10, 11, 11, 12, 13, 14, 15, 15), we will calculate the five-number summary: the minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

Data Set

\[ 6, 7, 8, 9, 9, 10, 10, 10, 11, 11, 12, 13, 14, 15, 15 \]

Statistical Measures

1. Minimum (Min):

   • The smallest value in the dataset: 6

2. First Quartile (Q1):

   • To find Q1, we look for the median of the first half of the data (not including the overall median since there's an odd number of data points).
   • The first half: \(6, 7, 8, 9, 9, 10, 10\) (7 values)
   • Q1 is the median of this first half:
   • Values: \(6, 7, 8, 9, 9, 10, 10\)
   • Median of first half = \(9\) (4th value)

3. Median (Med):

   • This is the middle value of the sorted dataset.
   • Since there are 15 values, the median is the 8th value: 10

4. Third Quartile (Q3):

   • To find Q3, we look for the median of the second half of the data (the overall median is included here).
   • The second half: \(10, 10, 11, 11, 12, 13, 14, 15, 15\)
   • Q3 is the median of this second half:
   • Values: \(10, 10, 11, 11, 12, 13, 14, 15, 15\)
   • Median of second half = \(12\) (4th value)

5. Maximum (Max):

   • The largest value in the dataset: 15

Summary of Statistical Measures

• Min: 6
• Q1: 9
• Med: 10
• Q3: 12
• Max: 15

Box Plot Creation

A box-and-whiskers plot will include the following elements:

• A box from Q1 (9) to Q3 (12).
• A line at the median (10).
• Whiskers extending to the minimum (6) and maximum (15).

Here is how you can visualize the box plot:

      6       9      10      12       15
------|-------|-------|-------|-------|------
       |       box    |       |       |
       |             med  |
       |                  |
    Min |          Q1      |           Q3            Max

Completed Summary

• Min: 6
• Q1: 9
• Med: 10
• Q3: 12
• Max: 15

You can create the box plot by placing the box between Q1 and Q3, with lines extending from the box to the minimum and maximum values.