Question

question 15 (5 points)
find the lower quartile of the following data set.
55, 60, 61, 61, 74, 75, 77, 81, 83, 87
74.5
81
87
61

Explanation:

Order and count the data set

The data set is already sorted in ascending order:

$$ 55, 60, 61, 61, 74, 75, 77, 81, 83, 87 $$

The total number of data values is:

$$ n = 10 $$

Find the median of the data set

Since \(n = 10\) is even, the median is the average of the 5th and 6th values:

$$ \text{Median} = \frac{74 + 75}{2} = 74.5 $$

Find the lower quartile (Q1)

The lower quartile is the median of the lower half of the data set (the first 5 values):

$$ 55, 60, 61, 61, 74 $$

Since there are 5 values (an odd number), the median of this lower half is the middle value (the 3rd value):

$$ Q_1 = 61 $$

Answer:

• (A) 74.5
• (B) 81
• (C) 87
• (D) 61 (Correct answer)