Video: Selecting a Given Mean’s Data Set

Which of the following data sets has a mean of 59? [A] 74, 79, 27, 59, 56 [B] 90, 64, 49, 13, 50 [C] 11, 50, 21, 72, 48 [D] 81, 34, 85, 21, 76 [E] 52, 76, 23, 50, 15.

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Video Transcript

Which of the following data sets has a mean of 59? A) 74, 79, 27, 59, 56; B) 90, 64, 49, 13, and 50; C) 11, 50, 21, 72, 48; D) 81, 34, 85, 21, 76; or E) 52, 76, 23, 50, and 15.

Okay, so in order to solve this problem, we want to find the mean of each of our data sets. So the mean, we got some mathematical notation here, which is 𝑥 bar, is equal to the sum of the values — so that’s the total of all the values — divided by the number of values in our data set. Okay, with this in mind, let’s go on and find the mean of each of our sets of data.

So for our first set of data, it’s gonna be 74 plus 79 plus 27 plus 59 plus 56 all divided by five which gives us 295 over five, which is equal to 59. Okay, great, we found the mean of our first set of data it’s actually 59. But it doesn’t say which of the following data sets has a mean of 59. So we’re gonna carry on and find the others just in case there’re more with a mean of 59.

For our second data set, when we add 90, 64, 49, 13, and 50, we get 266. So the mean is equal to 266 divided by five, which is equal to 53.2. So this one isn’t 59. So we can move on to the next data set. The sum of our next data set 11 plus 50 plus 21 plus 72 plus 48 is equal 202. So 202 divided by five gives us a mean of 40.4. So again, this isn’t equal to 59.

We can move on to the next data set. And the sum of the terms in this data set give us a total of 297. So the mean is 297 again divided by five, which is equal to 59.4, which is close, but it’s not exactly 59. So it’s looking like the first data set is probably gonna be the only one with a mean of exactly 59. But let’s double check and do our final data set.

So our final data set is 216 divided by five. Again, that’s because the sum of 52, 76, 23, 50, and 15 is 216, which gives us 43.2, which again isn’t equal to 59. So therefore, we can say that the data set A 74, 79, 27, 59, and 56 has a mean of 59.

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