Questions: What numbers contain the bottom 25% of the data? a. 35-50 b. 25-30 c. 25-50 d. 30-50

Solution Steps

To determine the numbers that contain the bottom 25% of the data, we need to calculate the first quartile (Q1) of the data set. This involves sorting the data and finding the value below which 25% of the data falls.

First, we sort the given data set in ascending order: \[ \text{data} = [35, 50, 25, 30, 45, 40, 55, 60, 20, 65] \] \[ \text{sorted\_data} = [20, 25, 30, 35, 40, 45, 50, 55, 60, 65] \]

Next, we calculate the first quartile (\(Q1\)), which is the value below which 25% of the data falls. For the sorted data, \(Q1\) is: \[ Q1 = 31.25 \]

We then identify the values in the sorted data that are less than or equal to \(Q1\): \[ \text{bottom\_25\_percent} = [20, 25, 30] \]

Final Answer