Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Let's calculate the measures of variability for the given data set step by step.
1. Order the Values:
The ordered data set is:
[tex]\[ 5, 17, 18, 20, 20, 21, 23, 26, 28, 29 \][/tex]
2. Median:
The middle value of the ordered data set (for 10 values) is the average of the 5th and 6th values.
[tex]\[ \frac{20 + 21}{2} = \frac{41}{2} = 20.5 \][/tex]
3. Range:
The range is the difference between the maximum and minimum values in the ordered data set.
[tex]\[ \text{Range} = 29 - 5 = 24 \][/tex]
So, the range is [tex]\(24\)[/tex] touchdowns.
4. Interquartile Range (IQR):
The interquartile range is the difference between the first quartile (Q1) and the third quartile (Q3).
- The first quartile ([tex]\(Q1\)[/tex]) is the median of the first half of the ordered data, excluding the overall median. The first half is:
[tex]\[ 5, 17, 18, 20, 20 \][/tex]
For these 5 values, the median (Q1) is the 3rd value:
[tex]\[ Q1 = 18.5 \][/tex]
- The third quartile ([tex]\(Q3\)[/tex]) is the median of the second half of the ordered data, excluding the overall median. The second half is:
[tex]\[ 21, 23, 26, 28, 29 \][/tex]
For these 5 values, the median (Q3) is the 3rd value:
[tex]\[ Q3 = 25.25 \][/tex]
- The interquartile range (IQR) is calculated as:
[tex]\[ \text{IQR} = Q3 - Q1 = 25.25 - 18.5 = 6.75 \][/tex]
Therefore:
- The range is [tex]\(24\)[/tex] touchdowns.
- The interquartile range is [tex]\(6.75\)[/tex] touchdowns.
1. Order the Values:
The ordered data set is:
[tex]\[ 5, 17, 18, 20, 20, 21, 23, 26, 28, 29 \][/tex]
2. Median:
The middle value of the ordered data set (for 10 values) is the average of the 5th and 6th values.
[tex]\[ \frac{20 + 21}{2} = \frac{41}{2} = 20.5 \][/tex]
3. Range:
The range is the difference between the maximum and minimum values in the ordered data set.
[tex]\[ \text{Range} = 29 - 5 = 24 \][/tex]
So, the range is [tex]\(24\)[/tex] touchdowns.
4. Interquartile Range (IQR):
The interquartile range is the difference between the first quartile (Q1) and the third quartile (Q3).
- The first quartile ([tex]\(Q1\)[/tex]) is the median of the first half of the ordered data, excluding the overall median. The first half is:
[tex]\[ 5, 17, 18, 20, 20 \][/tex]
For these 5 values, the median (Q1) is the 3rd value:
[tex]\[ Q1 = 18.5 \][/tex]
- The third quartile ([tex]\(Q3\)[/tex]) is the median of the second half of the ordered data, excluding the overall median. The second half is:
[tex]\[ 21, 23, 26, 28, 29 \][/tex]
For these 5 values, the median (Q3) is the 3rd value:
[tex]\[ Q3 = 25.25 \][/tex]
- The interquartile range (IQR) is calculated as:
[tex]\[ \text{IQR} = Q3 - Q1 = 25.25 - 18.5 = 6.75 \][/tex]
Therefore:
- The range is [tex]\(24\)[/tex] touchdowns.
- The interquartile range is [tex]\(6.75\)[/tex] touchdowns.
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.