In Exercises 13 and 14, find the mean, the median, and the mod...

Question

In Exercises 13 and 14, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why.

The responses of 1019 adults who were asked how much money they think they will spend on Christmas gifts in a recent year (Adapted from Gallup)

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Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So, first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A poll asked 870 adults how many books they read last year. The results were 10 or more books, 190, 3 to 9 books, 310, less than 3 books, 250, did not read any books, 120. Find the mean, median, and mode of the data, if possible, if any measure cannot be found or does not represent the center of the data, explain why. Awesome. So it appears for this particular problem, we're ultimately trying to solve for three separate answers. We're trying to determine the mean, median, and mode of this particular data set using our table that is provided to us by the problem itself. And It's important to note that we're asked to find these values if they can be possibly found, and if they cannot be found, we're asked to explain why we cannot determine that specific value. So, with that in mind, our first step in order to solve this particular problem, this particular problem is we're gonna focus on trying to solve for the mean first. So we need to recall a note. That for this particular prompt, based on the information we are given, we cannot, cannot calculate the exact mean because the data is grouped, and we do not know the exact number of books each person that each specific person that each person read within each group. So therefore, the mean cannot be calculated or cannot be found without estimation. So let's make a note of that. So I'll put The word mean and then I'll put a red X next to it because we cannot calculate the value for the mean. Because once again, we cannot calculate the exact mean value because our data is grouped. And because our data is grouped, we do not know the exact number of books that each individual person read within each group. So with that in mind, we cannot, we cannot determine our mean without some sort of estimation taking place. So, with that in mind, our next value that we need to solve for is the median. So, we need to note and recall that the total number of adults participating in this poll is 870. And we need to note that the median is the value at the 435th. And 436th positions. So, that will mean that we can determine the cumulative frequencies as did not read any books, so we need to note that those who did not read any books was 120, but less than 3 books, which I'll just call L3 for short. Is 120 + 250, which is equal to 370. And 3 to 9 books was 370. Plus 310, which is equal to 680. And 10 or more books, which I'll just call 10M for short, so 10 or more books is 680 plus 190, which when we add those two values together, we'll get 870. So, with that in mind, the 435th And 3 on our 436 people fall into the 3 to 9. Book group. Awesome. So let's make a note of that. I'll put it in a little fluffy cloud here. But we need to know once again that without a doubt that our 435th and 436. People will fall within our 3 to 9 books group. So now, moving right along here. Our next step is to solve for the mode. So as we should recall and note, the mode is the group with the highest frequency, which in this case is the 3 to 9, you know, 3 to 9 books group. And that is, or it's important to note that that consists of 310 people. So we need to state which measures cannot be found or do not represent at the center. And once again, as we should recall, the mean cannot be found exactly because the data is grouped and the median and mode can be found as the group 3 to 9 books. So once again, the meme cannot be found and the median and mode only specify the group, not the exact number of books. So with that in mind, our final pair of answers without a doubt will have to be, or rather our final set of answers will have to be. And here's a summary. Mean cannot be found because data is grouped, median 3 to 9 books group mode is 3 to 9 books group, and that's it. Those are our final pair or set of answers. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

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Key Concepts

Mean

Median

Mode

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