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In a data set, the values are: 1, 2, 3, 4, 5. What is the interquartile range?
In a data set, the values are: 1, 2, 3, 4, 5. What is the interquartile range?
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In a data set, the values are: 1, 2, 3, 4, 5. What is the interquartile range?
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Q1 = 2, Q3 = 4. Interquartile Range = Q3 - Q1 = 4 - 2 = 2.
Questions & Step-by-step Solutions
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Q
Q: In a data set, the values are: 1, 2, 3, 4, 5. What is the interquartile range?
Solution:
Q1 = 2, Q3 = 4. Interquartile Range = Q3 - Q1 = 4 - 2 = 2.
Steps: 7
Show Steps
Step 1: Arrange the data set in order. The values are already in order: 1, 2, 3, 4, 5.
Step 2: Find the median (Q2) of the data set. The median is the middle value. For 1, 2, 3, 4, 5, the median is 3.
Step 3: Divide the data set into two halves. The lower half is 1, 2 and the upper half is 4, 5.
Step 4: Find Q1 (the first quartile) which is the median of the lower half (1, 2). The median of 1, 2 is 1.5.
Step 5: Find Q3 (the third quartile) which is the median of the upper half (4, 5). The median of 4, 5 is 4.5.
Step 6: Calculate the interquartile range (IQR) using the formula: IQR = Q3 - Q1.
Step 7: Substitute the values: IQR = 4.5 - 1.5 = 3.
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