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Fourteen different​ second-year medical students at a hospital measured the blood pressure of the same person. The systolic readings​ (mm Hg) are listed below. Use the given data to construct a boxplot and identify the​ 5-number summary.

150
149
135
136
120
125
127
130
146
130
120
140
137
150

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Part 1
The​ 5-number summary is
  
enter your response here​,
  
enter your response here​,
  
enter your response here​,
  
enter your response here​, and
  
enter your response here​, all in mm Hg.
​(Use ascending order. Type integers or decimals. Do not​ round.)

1 answer

To construct a boxplot and identify the 5-number summary, we first need to sort the given blood pressure readings in ascending order and then find the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values.

The blood pressure readings in ascending order are: 120, 120, 125, 127, 130, 130, 135, 136, 137, 140, 146, 149, 150, 150.

Step 1: Identify the 5-number summary

  1. Minimum (Min): The smallest value in the data set.
    • Min = 120
  2. Maximum (Max): The largest value in the data set.
    • Max = 150
  3. Median (Q2): The middle value. Since there are 14 readings (an even number), the median is the average of the 7th and 8th values.
    • Median = (135 + 136) / 2 = 135.5
  4. First Quartile (Q1): The median of the first half of the data (the first 7 numbers).
    • Q1 = (125 + 127) / 2 = 126
  5. Third Quartile (Q3): The median of the second half of the data (the last 7 numbers).
    • Q3 = (140 + 146) / 2 = 143

Step 2: Compile the 5-number summary

Putting it all together:

  • Minimum = 120
  • Q1 = 126
  • Median (Q2) = 135.5
  • Q3 = 143
  • Maximum = 150

Summary

The 5-number summary is:

  • 120, 126, 135.5, 143, 150

Thus, your answer is:

  • The​ 5-number summary is 120, 126, 135.5, 143, and 150, all in mm Hg.