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Answer :
To find the interquartile range (IQR) of the given data set, we need to follow these steps:
1. Organize the Data:
Start by arranging the temperatures in ascending order:
40, 41, 41, 42, 43, 43, 44, 44, 45, 45.
2. Find the Median (Q2):
The median is the middle number in an ordered data set. Since we have 10 numbers, the median will be the average of the 5th and 6th numbers:
[tex]\[
Q2 = \frac{43 + 43}{2} = 43
\][/tex]
3. Divide the Data into Lower and Upper Halves:
The lower half consists of the numbers before the median:
40, 41, 41, 42, 43.
The upper half consists of the numbers after the median:
43, 44, 44, 45, 45.
4. Find Q1 (First Quartile):
The first quartile is the median of the lower half. Since there are 5 numbers, the median is the 3rd number:
[tex]\[
Q1 = 41
\][/tex]
5. Find Q3 (Third Quartile):
The third quartile is the median of the upper half. Similarly, with 5 numbers, the median is the 3rd number:
[tex]\[
Q3 = 44
\][/tex]
6. Calculate the Interquartile Range (IQR):
The interquartile range is the difference between Q3 and Q1:
[tex]\[
IQR = Q3 - Q1 = 44 - 41 = 3
\][/tex]
Therefore, the interquartile range of the data set is 3.
1. Organize the Data:
Start by arranging the temperatures in ascending order:
40, 41, 41, 42, 43, 43, 44, 44, 45, 45.
2. Find the Median (Q2):
The median is the middle number in an ordered data set. Since we have 10 numbers, the median will be the average of the 5th and 6th numbers:
[tex]\[
Q2 = \frac{43 + 43}{2} = 43
\][/tex]
3. Divide the Data into Lower and Upper Halves:
The lower half consists of the numbers before the median:
40, 41, 41, 42, 43.
The upper half consists of the numbers after the median:
43, 44, 44, 45, 45.
4. Find Q1 (First Quartile):
The first quartile is the median of the lower half. Since there are 5 numbers, the median is the 3rd number:
[tex]\[
Q1 = 41
\][/tex]
5. Find Q3 (Third Quartile):
The third quartile is the median of the upper half. Similarly, with 5 numbers, the median is the 3rd number:
[tex]\[
Q3 = 44
\][/tex]
6. Calculate the Interquartile Range (IQR):
The interquartile range is the difference between Q3 and Q1:
[tex]\[
IQR = Q3 - Q1 = 44 - 41 = 3
\][/tex]
Therefore, the interquartile range of the data set is 3.
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