Boxplots. In Exercises 29–32, use the given data to construct ...

Question

Boxplots. In Exercises 29–32, use the given data to construct a boxplot and identify the 5-number summary.

Blood Pressure Measurements Fourteen different second-year medical students at Bellevue Hospital measured the blood pressure of the same person. The systolic readings (mm Hg) are listed below.

138 130 135 140 120 125 120 130 130 144 143 140 130 150

Accepted Answer

Use the given data to construct a box plot and identify the 5 number summary. We have the reaction times. A group of 14 students participated in a reflex test where the reaction times and milliseconds were recorded. The recorded reaction times are as follows, and we have a data set here with the reaction times. We're also given a graph here to plot our box plotter. Now, to solve this, we'll find the 5 number summary, and we'll do this by first erasing the data and ascending order. I've done that here on the bottom. But we can first find the median. The median It's given by Q2. Which will be the middle data set value of our set. There are 14 values here, which means we have an even number. This will be the average of our 7th. And 8th, values. If we look at our dataset, we see that the 7th value. will be 260. And our 8th value is 265. The average from them, we will find by dividing by 2, to get 262.5. Now let's find our first quartile. Q1 will be the median of the lower half of our data set. We see then that we have 7 values, which means Q1 is 245. Q 3 Will be the median of the upper half of the set. And we see that this value is 280. We can now find the IQR, which is our inner quartile range. This will be the difference of Q3 and Q1. This is 280 minus 245, which gives us 35. Now we need to find possible outliers. We can do this by using the IQR. Our lower bound of outliers. is given by Q1. -1.5 multiplied by IQR. Which will be 245 minus 1.5, multiplied by 35. This gives us 192.5. The upper bounce Will be Q3 plus 1.5 multiplied by the IQR. This will be 280. Plus 1.5 multiplied by 35. This gives us 332.5. So if any value is lower than 192.5, Or greater than 332.5, this would be an outlier. But we see based on our data set, that none of these values fit in those ranges, which means there. Are no outliers. Now we can draw our box flat. We go back to our plot. We will first draw a small line at the minimum value. Which in our case, is 220. And one of the largest value of 310. No. We will draw a larger line at the median of 262.5. Which is roughly Right here You can also draw a large line at Q1, which is 245. And we can draw another large line at 280. For Q3. Now we just draw our bucks. We make a box to connect. Every line, and then we'll draw a line to connect our Macs and min. And this is our box fly. OK, I hope to help you solve the problem. Thank you for watching. Goodbye.

Key Concepts

Boxplot

Five-number summary

Quartiles

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