Using Technology to Find Quartiles and Draw Graphs In Exercise...

Question

Using Technology to Find Quartiles and Draw Graphs In Exercises 23–26, use technology to draw a box-and-whisker plot that represents the data set.

Hourly Earnings The hourly earnings (in dollars) of a sample of 21 employees at a consulting firm

25.89 27.09 31.76 28.28 26.19 27.43 24.06

25.61 22.56 29.76 18.01 23.66 38.24 37.27

32.70 31.12 25.87 15.06 23.12 30.62 19.85

Accepted Answer

All right, hello, everyone. So this question says, the following are the weekly study hours for a group of 21 college students. Draw a box and whisker plot for this data set. So, recall that before doing anything else, the data needs to be sorted in ascending order, from the smallest value to the largest. So here, I went ahead and did so in advance. So let me just go ahead and make this more visible. So from here, Let's begin by finding the median. Now the median. Is represented by the symbol Q2. And it refers to the value in the middle of the ordered list. So, because there are 21 data points in total, that's an odd number, the median is the 11th value. And that happens to be 14.9. So Q2 is equal to 14.9. Now we find our 1st and 3rd quartiles. Now, the first quartile, that's Q1, is the median of the lower half, but not including Q2. So it's the first half of the data set, not including 14.9. The median of the 10 values in the first half is the average of the 5th and 6th values. So the fifth and 6th values are 12.5 and 12.9. So that's the sum of 12.5 and 12.9 divided by 2. Which equals 12.7. So Q1 is equal to 12.7. And now we look for Q3. That's the 3rd oops. The 3rd quartile So, the 3rd quartile is the median of the upper half, but again, not including Q2. So, because there's an even number of data points in the upper half, the median is once again going to be the average of the 5th and 6th values. So that's 17.2 and 17.6. Actually I miscounted, so let me correct myself. It's actually 16.8 and 17.2. So Q3 is equal to the sum of 16.8 and 17.2, divided by 2. Which equals 17.0. So now what you want to do is identify if there are any outliers, and to do so, you need to find the interquartile range. So the IQR. is equal to Q3 subtracted by Q1. So 17.0, subtracted by 12.7. Equals 4.3. So, based on this, right, recall that if a value is less than Q1 subtracted by 1.5, multiplied by the IQR. Or greater than Q3 added to 1.5 multiplied by the IQR, that number is considered an outlier. So 12.7. Subtracted by 1.5, multiplied by 4.3. Is equal to 6.25. And on the other hand, 17.0. Added to 1.5, multiplied by 4.3. Is equal to 23.45. So based on this, because no value in the data set is less than 6.25 or greater than 23.45, there are no outliers in this data set. So now we have the 5 values necessary to create the box and whisker plot. Because keep in mind that you also need to point out. The minimum and the maximum. So the minimum, the smallest number in the data set is 10.1. And the maximum is 19.7. So onto The box and whisker plot. So your first step, if you recall, is to construct a horizontal axis. Hopefully. With a line that's straighter than the one I just drew. But After drawing the horizontal axis, you label the axis with values that cover the range of the data set. And then you plot the 5 numbers below the axis, or excuse me, above the axis. So recall that the 5 numbers you're plotting are the minimum, the maximum, and Q1, Q2 and Q3. So, the box of the box and whisker plot spans from Q1. To Q3. With a vertical line segment inside of the box to represent Q2. And so the whiskers from the box represent the minimum and maximum values. So, after all is said and done, the box and whisker plot that's listed in your final answer, which is much nicer than mine, is as follows. And there you have it. So with that being said, thank you so very much for watching. And I hope you found this helpful.

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Key Concepts

Quartiles

Box-and-Whisker Plot

Using Technology for Data Analysis

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