In a data set, the values are: 1, 2, 3, 4, 5. What is the interquartile range?

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Question: In a data set, the values are: 1, 2, 3, 4, 5. What is the interquartile range?

Options:

Correct Answer: 2

Solution:

Q1 = 2, Q3 = 4. Interquartile Range = Q3 - Q1 = 4 - 2 = 2.

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?

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.

Interquartile Range (IQR) – The interquartile range is a measure of statistical dispersion, calculated as the difference between the third quartile (Q3) and the first quartile (Q1) of a data set.
Quartiles – Quartiles are values that divide a data set into four equal parts, with Q1 being the median of the first half and Q3 being the median of the second half.