A researcher conducts a study comparing two different treatments with a sample of n = 16

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Find the range and mean of each data set. Use your results to compare the two data sets. $$ \begin{array}{l}{\text { Set } A: 0 \quad 12 \text { 7 } 1921} \\ {\text { Set B: } 13 \text { 16 } 15 \text { 17 } 12}\end{array} $$

Sheila P.

Intro Stats / AP Statistics 3 months, 3 weeks ago

23. A researcher conducts a study comparing two different treatments with a sample of n = 16 participants in each treatment. The study produced the following data: Treatment 1: 6,7,11,4,19,17,2,5,9, 13,6,23, 4,6, Treatment 2: 10,9,6,6,1, 11, 8,6,3,2, 11,1,12,7,10,9 a. Calculate the mean for each treatment. Based on the two means,which treatment produces the higher scores? b. Calculate the median for each treatment: Based on the two medians, which treatment produces the higher scores? Calculate the mode for each treatment. Based on the two modes,which treatment produces the higher scores?

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Alli B.

Washington University in St Louis

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Video Transcript

So for this problem we are given two sets of data. Both pieces are both sets of data have the same number of points through 16 points in each a set of data here. And were asked to calculate the mean median mode for the two sets of data and then find which one is bigger. Um The first thing I did is down in blue here, I rewrote the data in order. I think it's really annoying that the data isn't given in order because honestly I think that's the place you're most likely to make a mistake on this question. So now that we've reordered the data in order we can calculate the three things. So how do we find the mean? We take the some of all the points and then we divide by the number of points. So I found this on in advance because you don't need to watch me type everything in my calculator, but it's really easy. I just literally hit six plus seven plus 11 plus four, I add them all up. So for the first one I got 144, that's my son, The number of points is 16. So that's how I'm going to calculate it and then I'm just going to type that into my calculator And that comes out evenly, which is really nice. So the mean is nine for T one. Um for T. two. Again I did this summer, I just added them up all together. The sum was 112, there's still 16 points. And then I'm going to type that fraction into my calculator again. And The people really helped us out when they were setting up, that's equal to 7:00 AM. So when we're comparing the means, I would say that T. one has the higher mean higher scores for T. one. Now the mean the median is finding the middle point. So to find the media and we're going to look down at our blue set of data that's in order. Um And we're going to just pair off the numbers were just going to cross them out top and bottom until we get to the middle. So my first pair for T. one is one in 23 across second pair, third pair, fourth pair MS Perry sixth pair, 7th pair. No, because we have an even number of data points to start with, we're left with two numbers in the middle. So the medium is actually going to be the average of those two numbers. So what's halfway between six and seven? 6.5 now, we're gonna repeat the same process on our second set of data. Cross out a pair of numbers, hair pair, repair parents There. And similarly, we're left with two numbers here. Um halfway between seven and eight, that's going to be 7.5. So for the median T to give higher scores. Um Lastly the mode now for this particular set of data are mode is not occurring particularly frequently. So I don't really think this would be a good way to compare the data sets. But the mode is the number that appears most often, mm hmm. Um, so we're looking for repeated numbers, repeated numbers in our data set. For both of these sets, there's only one number that repeats three times and that's six. So for both datasets are mode and six. And so for that last question, these two are equal.