Questions: Section 3.3 Homework Question 4.33.32 Points 0 of 1 For the following integer special medical students in a hospital measured the blood pressure of this same person. The systolic readings (mm Hg) are listed below. Use the given data to construct a boxplot and identify the outliers, if any. 137, 138, 135, 128, 120, 125, 119, 130, 148, 144, 125, 127, 140 This 5-number summary is: Type in integers or decimals. Do not round. Minimum: Q1: Median: Q3: Maximum:

Solution Steps

To solve this problem, we need to calculate the five-number summary (minimum, Q1, median, Q3, maximum) of the given systolic readings. We will then use these values to construct a boxplot and identify any outliers.

1. Sort the data: Arrange the systolic readings in ascending order.
2. Calculate the five-number summary:
   • Minimum: The smallest value in the sorted list.
   • Q1 (First Quartile): The median of the first half of the data.
   • Median: The middle value of the sorted list.
   • Q3 (Third Quartile): The median of the second half of the data.
   • Maximum: The largest value in the sorted list.
3. Construct the boxplot: Use the five-number summary to create the boxplot.
4. Identify outliers: Outliers are typically defined as values that are below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR, where IQR (Interquartile Range) is Q3 - Q1.

First, we need to organize the given systolic readings in ascending order.

Given data: \(137, 138, 135, 128, 120, 125, 119, 130, 148, 144, 125, 127, 140\)

Sorted data: \(119, 120, 125, 125, 127, 128, 130, 135, 137, 138, 140, 144, 148\)

The minimum value is the smallest number in the sorted list, and the maximum value is the largest number.

\[ \text{Minimum} = 119 \] \[ \text{Maximum} = 148 \]

The median is the middle value of the sorted list. Since there are 13 values, the median is the 7th value.

\[ \text{Median} = 130 \]

Q1 (the first quartile) is the median of the first half of the data (excluding the overall median if the number of data points is odd). Q3 (the third quartile) is the median of the second half of the data.

First half (excluding the median): \(119, 120, 125, 125, 127, 128\)

\[ \text{Q1} = \frac{125 + 125}{2} = 125 \]

Second half (excluding the median): \(135, 137, 138, 140, 144, 148\)

\[ \text{Q3} = \frac{138 + 140}{2} = 139 \]

Final Answer