The data set represents the number of minutes a sample of 27 p...

Question

The data set represents the number of minutes a sample of 27 people exercise each week.

108 139 120 123 120 132 123 131 131

157 150 124 111 101 135 119 116 117

127 128 139 119 118 114 127 142 130

g. Display the data using a box-and-whisker plot.

Accepted Answer

Hi everyone. Let's take a look at this practice problem. This problem says the following data set shows the number of hours 190 employees worked last week, and we're getting the values of 32, 35, 40, 38, 36, 37, 39, 41, 34, 33, 42, 36, 38, 40, 37, 39, 35, 34, and 41. Summarize the data by creating a box and whisker plot. So in order to create our box and whisker plot, the first thing we need to do is order our data in ascending order. In doing so, we will get 32. 33. 34. 34 again. 35, 35 again. 36 36 again. 37 37 again. 38 38 again. 39 39 again. 40 40 again. 41. 41 again, and finally 42. So now that we have our data ordered, we're going to use it to determine a couple of values that we need to create our box and whisker plot. So the first value we need to find is our median, and we call that the median is going to be the value that appears in the middle of our data set. And so our median, which we'll label as Q2. It's going to be equal to the 10th value in our data set, since we have a total of 19 values. And we look at the 10th value, that turns out to be 37. So that means that Q2 is going to be equal to 37. Now we're going to need to find our first quartile, Q1. I recall that the first quartile is going to be the median of the first half of our data, so the data that is actually below our median. And so here we'll actually have 9 data points. So the value in the middle would be the 5th data point. And so when we look at the 5th data point in this data set, we see that it turns out to be 35. So that means our first quartile Q1 is going to be equal to 35. We do something similar for our third quartile, Q3. Recall that this is going to be the median of the upper half of our data, so the data that is above the median. And so, again, we'll have 9 data points, and here we're gonna be looking again for the 5th data in this data set. And that actually turns out to be 40. So that means that Q3 is going to be equal to 40. And we're also going to need to determine if we have any outliers in our data set. And to do that, we need to calculate our interquartile range, which is going to be uh label it as IQR. And we call that our interquartile range, is equal to Q3 minus Q1. Which in our case, plugging in the values will have 40 minus 35, which is equal to 5. So we'll now use this to determine the upper bound and lower bounds for our outliers. So, starting off with the lower bound, which we'll label as LB. And that's going to be equal to, and here we call your definition for our lower bound. It's going to be Q1 minus 1.5, multiplied by our interquartile range IQR. Substituting in our values, this is going to be equal to 35 minus 1.5, multiplied by 5. Which is equal to 27.5. We'll do something similar for our upper bound, which we'll label as UB, and recall that for this definition, it is going to be equal to Q3 plus 1.5 multiplied by our interquartile range IQR. So again, substituting in our values, this is going to be equal to 40 plus 1.5, multiplied by 5, which is equal to 47.5. And so we're looking for values in our data set that are below 27.5 and above 47.5. However, all of our data values fall between our lower bound and upper bound, so that means that we have no outliers. So we now have enough information to create our box and whisker plot. So the first thing we're going to do is draw a number line, and we'll start off with a value of 28 and label every. Two values, all the way up to 44. So we'll have 28, then 30. Then 32. Then 34. Then 36. Then 38. Then 40? Then 42, and then finally. 44 So next we're going to draw the box portion of our box and whisker plot, and recall that our box goes from Q1 to Q3. So, we're going to draw the left side of our box at a value of 35, and the right side of our box at a value of 40. So that is going to be our box. Now, inside the box, we're gonna have a vertical line to denote our median, which is at 37. So we'll draw a vertical line at a value of 37. And so now we need to draw our whiskers, and we call that our whiskers. are determined by the minimum and maximum values that are not outliers. So on the left hand side of our box, we'll have a whisker that is at 32, and so we'll draw a short little line there and connect that with a horizontal line to the left side of our box. Since 32 is our minimum value, that is not an outlier. We'll do the same thing on the right hand side of our box for the other whisker, and so here we'll have a maximum value of 42 in our data set. And so we'll draw a short vertical line at 42 and connect it to the right side of our box with a horse on line for our other whisker. And so the graph that we have created on the screen here is going to be the answer to this problem. So, I hope that this explanation has been useful, and I'll see you in the next video.

The data set represents the number of minutes a sample of 27 people exercise each week.
108 139 120 123 120 132 123 131 131
157 150 124 111 101 135 119 116 117
127 128 139 119 118 114 127 142 130

g. Display the data using a box-and-whisker plot.

Key Concepts

Box-and-Whisker Plot

Quartiles

Interquartile Range (IQR)

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