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Sagot :
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.
### 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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