Finding a Percentile In Exercises 33–36, use ...

Question

Finding a Percentile In Exercises 33–36, use the data set, which represents the ages of 30 executives.

43 57 65 47 57 41 56 53 61 54

56 50 66 56 50 61 47 40 50 43

54 41 48 45 28 35 38 43 42 44

Which ages are above the 75th percentile?

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says the following are the ages of 24 participants in a workshop, and we're given the values of 1819, 2021, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, and 41. Which ages are above the 75th percentile? Now, if we look at our data, we see that it is already ordered, and we're just going to rewrite it so that it all shows up on a single line. Though we have the values of 1819. 20 21 22. 23 24. 25 26. 27 28 29 30. 31 32. 33 34. 35 36 37 38 39 40 And 41. Now, we're looking for ages above the 75th percentile. Now the 75th percentile corresponds to our third quartile. And so, what we really need to do is to find the value of our 3rd quartile and see which values in our ages here fall above that. So we call that the 3rd quartile is going to be the median of the upper half of our data set. And so, since here we have 24 participants, the upper half is going to be the upper 12 values, so that's going to be between 30 and 41. And so here we need to find the median of this data set, and since we have 12 values here, we have an even number of data points. So we're actually going to be finding the midpoint between the two values in the middle. The two values in the middle correspond to 35 and 36, so we need to find the midpoint of this, and that's going to be our third quartile. So our third quartile, Q3, is going to be equal to, and here we call how to find a midpoint between two points, and that is going to be to add the two values together. So we'll have 35 plus 36, and we'll take that quantity and divide it by 2. That means that Q3 is going to be equal to 35.5. So we need to have all ages that are above 35.5. And that means that we're just going to have the ages of 36. 37 38 39 40 And 41. So that is going to be the answer for this problem. So I hope that this explanation has been useful, and I'll see you in the next video.

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Finding a Percentile In Exercises 33–36, use the data set, which represents the ages of 30 executives.
43 57 65 47 57 41 56 53 61 54
56 50 66 56 50 61 47 40 50 43
54 41 48 45 28 35 38 43 42 44

Which ages are above the 75th percentile?

Key Concepts

Percentiles

Data Set

Calculating Percentiles

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Finding a Percentile In Exercises 33–36, use the data set, which represents the ages of 30 executives.43 57 65 47 57 41 56 53 61 5456 50 66 56 50 61 47 40 50 4354 41 48 45 28 35 38 43 42 44Which ages are above the 75th percentile?