Questions: 3.3.3 Quiz: Box Plots Question 4 of 10 If there are 21 values in a data set in order from smallest to largest, what is the first quartile of the data set? A. The mean of the 5th and 6th values B. The mean of the 6th and 7th values C. The mean of the 3rd and 4th values D. The mean of the 4th and 5th values

Solution Steps

The first quartile (\( Q_1 \)) is the value that separates the lowest 25% of the data from the rest. For a data set with \( n = 21 \) values, the position of \( Q_1 \) can be calculated using the formula: \[ Q_1 = \frac{n + 1}{4} \] Substituting \( n = 21 \): \[ Q_1 = \frac{21 + 1}{4} = 5.5 \] This means \( Q_1 \) is the average of the 5th and 6th values in the ordered data set.

From the given options:

• A. The mean of the 5th and 6th values
• B. The mean of the 6th and 7th values
• C. The mean of the 3rd and 4th values
• D. The mean of the 4th and 5th values

The correct option is A, as it matches the calculation in Step 1.

The first quartile of the data set is the mean of the 5th and 6th values. Therefore, the correct answer is A.

Final Answer