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Numerade Educator

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Problem 19 Hard Difficulty

The table shows the number of correct answers on a test consisting of 15 questions. Find the mean, the median, and the mode for the number of correct answers.
$$
\begin{array}{|c|c|c|c|c|c|c|c|}\hline \text { Correct } & {6} & {7} & {8} & {9} & {11} & {12} & {13} & {14} & {15} \\ \hline \text { Frequency } & {1} & {0} & {1} & {3} & {5} & {8} & {9} & {6} & {5} & {2} \\ \hline\end{array}
$$

Answer

Mean$=11.625$
Median$=12$
Mode$=12$

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Video Transcript

So for number 19 were given the situation of correct answers and how often that occurred for each amount. And so we were asked to find the mean, needing the mode, using this application type of problem. So it's gonna work the same way as we've done before, where we need to. First of all, in order to find the mean, add up all the numbers in the frequency columns organ add up one plus zero plus one plus three plus five plus eight plus nine plus six plus five plus two. And you're going to get a total of 40. Yes, that we're gonna type 40 year put a 40 here, and that's gonna be an additional road that you want to add to your, uh, your list or your table and that in order to continue to work on trying to find the mean we need to go ahead and do the correct number times the amount of times it occurs. So, for instance, six times one. So we're gonna go ahead and just do that here in this additional column that you'll need to add so six times 1267 times 00 eight times one is eight. Nine times three is 27 10 times five is 50 11 times eight is 88. Okay. And then we've got 12 times nine is 108 13 times six is 78. 14 times five is 70 and 15 times two is 30. 30. And so now, in order to continue and try and find the meeting that we need to now add up all the numbers that were the correct numbers times the function. So we're gonna add up all of these numbers in this column. So what to do? 30 plus 70 or 78 plus one? +08 plus 88 plus 50 plus 27. Plus eight and six. That's going to get us 465. Lastly, in order, go find the mean We need Teoh Teik The big number, the 4 65 and decided by the little number four. Certainly 4 65 Divided by 40. And that's going to get us out. 11 Hope, 11.6 to 5. Rights. 11.6 to 5. Have a nice way. All right. And then for the median, we're going to need to go get the cumulative frequency. That's an additional column that needs to be added. So the cumin of frequency you started out of the bottom or the top, um, and work your way down or up, depending on where you start. So we're gonna start on the bottom and work our way up. So you start off by writing the first number. So then you're going to take your first number and add it. The next number that was in the frequencies of five in this case or two plus five is seven that's gonna go here next is going to take that seven and that six and add it. That's gonna go here. 13 plus nine is going to get me 22 22 8 is going to get me 30. 30 plus five is going to get me 35 35 plus three is gonna get me 38 and one is going to get me 39 and then remember their numbers years will keep it 39 my last number is gonna be forward. E. So the main reason we do this is we take our median, um, is gonna have to be halfway between our 40 frequency. So halfway 40 is 20. So we're looking for where that jump happens between, um, for that 20 to occur, and that's gonna happen from that 13 to 22. So that means 12 is gonna have to be our median because of how it jumps from that 13 to 22 so that that median of 20 is happening and occurring here at that correct number of 12. And then it also turns out that our mode, the number that occurs the most according to our frequency nine is the highest number that occurred nine times. And so that 12 occurred nine times. And so that's gonna be our mode as well. Yeah.