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, 9, comma, 10, comma, 12, comma, 13, comma, 13, comma, 13, comma, 15, comma, 16
6,7,8,9,9,9,10,12,13,13,13,15,16
Min:
Q1:
Med:
Q3:
Max:

Answer 1

To determine the statistical measures for the given data set \(6, 7, 8, 9, 9, 9, 10, 12, 13, 13, 13, 15, 16\), we can follow these steps:

1. Min: The minimum value in the data set is \(6\).

2. Max: The maximum value in the data set is \(16\).

3. Median: To find the median, we first count the number of data points. There are 13 data points, which is odd, so the median is the middle value. The middle position is at \((13 + 1)/2 = 7\). The value in the 7th position is \(10\).

4. Q1 (First Quartile): Q1 is the median of the first half of the data. The first half consists of the values: \(6, 7, 8, 9, 9, 9\). There are 6 values, so we take the average of the 3rd and 4th values: \( (8 + 9)/2 = 8.5 \).

5. Q3 (Third Quartile): Q3 is the median of the second half of the data. The second half consists of the values: \(12, 13, 13, 13, 15, 16\). There are also 6 values, so we take the average of the 3rd and 4th values: \( (13 + 13)/2 = 13 \).

Now to summarize the results:

• Min: \(6\)
• Q1: \(8.5\)
• Med: \(10\)
• Q3: \(13\)
• Max: \(16\)

Summary of Statistical Measures:

• Min: 6
• Q1: 8.5
• Med: 10
• Q3: 13
• Max: 16

Box and Whiskers Plot

To create a box and whiskers plot:

• The box will extend from \(Q1\) (8.5) to \(Q3\) (13).
• A line in the box at the median (10).
• Whiskers will extend from the minimum (6) to \(Q1\) and from \(Q3\) to the maximum (16).

When you create the plot:

• Draw a box from 8.5 to 13,
• Mark a line at 10 inside the box,
• Extend lines (whiskers) from 6 to 8.5 on one side and from 13 to 16 on the other.

This is how you can visualize the distribution of the data effectively using a box and whiskers plot.