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The data set below represents the total number of touchdowns a quarterback threw each season for 10 seasons of play.

[tex]\[ 29, 5, 26, 20, 23, 18, 17, 21, 28, 20 \][/tex]

1. Order the values:

[tex]\[ 5, 17, 18, 20, 20, 21, 23, 26, 28, 29 \][/tex]

2. Determine the median:

[tex]\[ \frac{20 + 21}{2} = \frac{41}{2} = 20.5 \][/tex]

Calculate the measures of variability for the data set.

The range is [tex]\(\square\)[/tex] touchdowns.

The interquartile range is [tex]\(\square\)[/tex] touchdowns.



Answer :

GinnyAnswer
Let's proceed step by step with the information provided:

### 1. Order the values:
The ordered values are:
[tex]\[ 5, 17, 18, 20, 20, 21, 23, 26, 28, 29 \][/tex]

### 2. Determine the median:
Since the data set contains 10 values (an even number), the median is the average of the 5th and 6th values in the sorted list.
[tex]\[ \text{5th value} = 20 \][/tex]
[tex]\[ \text{6th value} = 21 \][/tex]
[tex]\[ \text{Median} = \frac{20 + 21}{2} = \frac{41}{2} = 20.5 \][/tex]

### Calculate the measures of variability:

#### The Range:
The range is the difference between the maximum and minimum values in the data set.
[tex]\[ \text{Maximum value} = 29 \][/tex]
[tex]\[ \text{Minimum value} = 5 \][/tex]
[tex]\[ \text{Range} = 29 - 5 = 24 \][/tex]

#### The Interquartile Range (IQR):
The Interquartile Range (IQR) is the difference between the 75th percentile (Q3) and the 25th percentile (Q1).

To find Q1 and Q3, we need to determine the values at the 25th percentile and 75th percentile positions.

For Q1 (25th percentile), we have:
[tex]\[ Q1 = 18.5 \][/tex]

For Q3 (75th percentile), we have:
[tex]\[ Q3 = 25.25 \][/tex]

[tex]\[ \text{IQR} = Q3 - Q1 = 25.25 - 18.5 = 6.75 \][/tex]

So, the measures of variability are:
- The range is [tex]\( 24 \)[/tex] touchdowns.
- The interquartile range (IQR) is [tex]\( 6.75 \)[/tex] touchdowns.