Tail lengths (in feet) for a sample of American alligators are...

Question

Tail lengths (in feet) for a sample of American alligators are listed.

6.5 3.4 4.2 7.1 5.4 6.8 7.5 3.9 4.6

a. Find the mean, median, and mode of the tail lengths. Which best describes a typical American alligator tail length? Explain your reasoning.

Accepted Answer

Welcome back, everyone. The daily high temperatures in degrees Celsius for a week in our city are 22, 24, 21, 23, 25, 24, and 22. Find the mean, median, and mode of the temperatures, which measure best represents a typical day's high temperature? Justify your answer. Now, before we start, let's first arrange our data in order, OK? That will help us to easier read, OK. It to easier read the information that we have, OK? So now, in ascending order, OK, our data is gonna be 21. So let me put a call on here actually. It's gonna be 21. We're gonna have 22 twice. Then 23. Then 24 twice, OK, and then 25. And again, like we said, it would just make it easier to refer to our data when we're finding or, or, or different types of averages. OK? Now let's start with the mean. The mean is found by dividing the sum of all values by the number of values. So in that case, the mean is gonna be 22 + 24 + 21 + 23 + 25 plus 24 + 22, OK. All divided. By 7 because there are 7 values. And in that case, when we add those up, that's 161 and 161 divided by 7 is 23. Therefore, the mean. Is 23 °C. Next, what about the median? Well, recall that the median is the middle value when the data set is ordered from least to greatest. And if there's an even number of values, it is the average of the two middle values. Notice that we have 7 values and we already have them in order, so the median will be the 4th value. So starting from 21, we have 21, 22, 23, 21, 22, 22, and 23. 23 is the 4th value. Therefore, that means the median. Is 23 °C. Next, what about the mode? Well, recall that the mode is the value that appears most frequently. When we go to our data set, notice that 22 appears twice and 24 appears twice, where the rest appear only once. So in this case we say that our data set is bimodal. In other words, it has two modes, OK, where the modes are 22 °C. And 24 °C. Now, from our measures, which one best represents a typical day's high temperature? Well, notice that the mean and median are both 23 °C, and the data is symmetrical without all layers. Therefore, the mean or median, OK, the mean or median best represent a typical day's temperature. But the best represent a typical day's temperature. And do you remember why we said that? Because the data is symmetrical. OK. Without all layers. See, if it had all layers, then it would have affected the mean, and that probably wouldn't be the best. And here, because our data is symmetrical, then our median is also appropriate. Thus, this is the reason why we can choose these choose 23 °C as a typical day's temperature. Thanks a lot for watching everyone. I hope this video helped.

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Tail lengths (in feet) for a sample of American alligators are listed.
6.5 3.4 4.2 7.1 5.4 6.8 7.5 3.9 4.6

a. Find the mean, median, and mode of the tail lengths. Which best describes a typical American alligator tail length? Explain your reasoning.

Key Concepts

Mean

Median

Mode

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Tail lengths (in feet) for a sample of American alligators are listed.6.5 3.4 4.2 7.1 5.4 6.8 7.5 3.9 4.6a. Find the mean, median, and mode of the tail lengths. Which best describes a typical American alligator tail length? Explain your reasoning.