Question

A teacher surveyed her class after they had taken a vocabulary test. Eighteen of the students claimed they had studied at least one hour for the test. The remaining twelve students admitted that they had not studied for the test at all. The test results (expressed as a percent) for the two groups are shown below. Studied: 87, 100, 94, 79, 92, 100, 95, 83, 89, 99, 100, 91, 89, 95, 100, 93, 96, 83 Did Not Study: 82, 72, 45, 91, 58, 83, 65, 87, 90, 77, 73, 89 Part 1: Calculate the mean of the group that did not study, rounded to the nearest tenth. Part 2: Calculate the mean absolute deviation of the group that did not study, rounded to the nearest tenth. Part 3: How many of the scores (from the group that did not study) are more than two mean absolute deviations from the mean?

          A teacher surveyed her class after they had taken a vocabulary test. Eighteen of the students claimed they had studied at least one hour for the test. The remaining twelve students admitted that they had not studied for the test at all. The test results (expressed as a percent) for the two groups are shown below.
Studied: 87, 100, 94, 79, 92, 100, 95, 83, 89, 99, 100, 91, 89, 95, 100, 93, 96, 83
Did Not Study: 82, 72, 45, 91, 58, 83, 65, 87, 90, 77, 73, 89
Part 1: Calculate the mean of the group that did not study, rounded to the nearest tenth.
Part 2: Calculate the mean absolute deviation of the group that did not study, rounded to the nearest tenth.
Part 3: How many of the scores (from the group that did not study) are more than two mean absolute deviations from the mean?

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Added by Cristina A.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Cheryl Glor

02/17/2023

Step 1

To calculate the mean, add up all the scores and then divide by the number of scores. The scores for the group that did not study are: 82, 72, 45, 91, 58, 83, 65, 87, 90, 77, 73, 89. First, add all the scores together: 82 + 72 + 45 + 91 + 58 + 83 + 65 + 87 + 90 + Show more…

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A teacher surveyed her class after they had taken a vocabulary test. Eighteen of the students claimed they had studied at least one hour for the test. The remaining twelve students admitted that they had not studied for the test at all. The test results (expressed as a percent) for the two groups are shown below. Studied: 87, 100, 94, 79, 92, 100, 95, 83, 89, 99, 100, 91, 89, 95, 100, 93, 96, 83 Did Not Study: 82, 72, 45, 91, 58, 83, 65, 87, 90, 77, 73, 89 Part 1: Calculate the mean of the group that did not study, rounded to the nearest tenth. Part 2: Calculate the mean absolute deviation of the group that did not study, rounded to the nearest tenth. Part 3: How many of the scores (from the group that did not study) are more than two mean absolute deviations from the mean?

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Transcript

00:01 Here we have a group of data of 12 data points of students who did not study, and these are their test scores.

00:06 The first thing we have to do is find the mean.

00:09 So in order to do that, we're going to sum up all of the individual test scores, and then we're going to divide by the number of the test scores that are present in our dataset.

00:21 So i'm just going to rewrite all of those out, and i'm going to be running out a room.

00:26 So i'm going to actually, you know what, i will put them over here, and hopefully we won't run into some problems later.

00:33 So then we have 12 data points.

00:37 So we'll divide by 12.

00:38 So let's do that now.

00:40 We have 82 plus 72 plus 45 plus 91 plus 58 plus 83.

00:47 Then we add 65, 87, 97, and then 89.

00:54 And we get a total of 912.

00:59 So now what we're going to do is we're going to divide our total or our sum by 12.

01:07 And our mean is going to be 76.

01:11 And we need to get it to the nearest 10th.

01:13 So it will be 76 .0.

01:15 Now we have to find the mean absolute deviation.

01:19 And in order to do that, we need to find the absolute values for all of our scores or the deviation from the mean for all of our scores.

01:27 So what we're going to do is we're going to subtract 76 from each one of our scores.

01:33 And we will find the amount that the score deviates from the mean.

01:38 So let's do that.

01:39 We have 82 minus 76.

01:41 Well, that's going to be six.

01:43 The next one's going to be minus four...

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