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Set 1: [tex]\(21, 24, 36, 38, 40, 42, 44, 63, 85\)[/tex]
- Lower quartile [tex]\(= 30\)[/tex]
- Median [tex]\(= 40\)[/tex]
- Upper quartile [tex]\(= 53.5\)[/tex]

Set 2: [tex]\(0, 4, 10, 16, 28, 50, 72, 100\)[/tex]
- Lower quartile [tex]\(= 7\)[/tex]
- Median [tex]\(= 22\)[/tex]
- Upper quartile [tex]\(= 61\)[/tex]

Find the interquartile range (IQR) for each set and determine which set shows a larger spread near the median.

Set 1:
Interquartile range (IQR) [tex]\(= \square\)[/tex]

Set 2:
Interquartile range (IQR) [tex]\(= \square\)[/tex]



Answer :

GinnyAnswer
Sure, let's find the interquartile range (IQR) for each set and then compare them. The interquartile range is the difference between the upper quartile (Q3) and the lower quartile (Q1).

### Set 1:
- Lower Quartile ([tex]\(Q1\)[/tex]) = 30
- Upper Quartile ([tex]\(Q3\)[/tex]) = 53.5

The interquartile range (IQR) is calculated as:
[tex]\[ \text{IQR} = Q3 - Q1 \][/tex]
[tex]\[ \text{IQR} = 53.5 - 30 \][/tex]
[tex]\[ \text{IQR} = 23.5 \][/tex]

So, the interquartile range for Set 1 is [tex]\(23.5\)[/tex].

### Set 2:
- Lower Quartile ([tex]\(Q1\)[/tex]) = 7
- Upper Quartile ([tex]\(Q3\)[/tex]) = 61

The interquartile range (IQR) for Set 2 is calculated as:
[tex]\[ \text{IQR} = Q3 - Q1 \][/tex]
[tex]\[ \text{IQR} = 61 - 7 \][/tex]
[tex]\[ \text{IQR} = 54 \][/tex]

So, the interquartile range for Set 2 is [tex]\(54\)[/tex].

### Comparison:
- Set 1 interquartile range = [tex]\(23.5\)[/tex]
- Set 2 interquartile range = [tex]\(54\)[/tex]

Larger Spread Around the Median:
The interquartile range for Set 2 is larger, indicating that Set 2 has a greater spread of values around the median compared to Set 1. Therefore, Set 2 shows a larger spread near the median.

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