Math 1 Mean Absolute Deviation

1. Sherrie just registered for her wedding. So far 6 items have been fulfilled on her registry. Find the mean price of the fulfilled items. $29, $58, $15, $129, $75, $22

43.5

129

54.7

114

The mean price of the fulfilled items can be found by adding up the prices of all the items and then dividing by the total number of items. In this case, the sum of the prices is $29 + $58 + $15 + $129 + $75 + $22 = $328. There are a total of 6 items, so dividing the sum by 6 gives us $328/6 = $54.7. Therefore, the mean price of the fulfilled items is $54.7.

Explanation

The mean price of the fulfilled items can be found by adding up the prices of all the items and then dividing by the total number of items. In this case, the sum of the prices is $29 + $58 + $15 + $129 + $75 + $22 = $328. There are a total of 6 items, so dividing the sum by 6 gives us $328/6 = $54.7. Therefore, the mean price of the fulfilled items is $54.7.

2. Find the mean absolute deviation for the set below. S = {85, 90, 68, 75, 79}

79.4

6.48

32.4

79

The mean absolute deviation (MAD) is a measure of the average distance between each data point and the mean of the set. To find the MAD, we first calculate the mean of the set, which is (85+90+68+75+79)/5 = 79.4. Then, we find the absolute difference between each data point and the mean: |85-79.4| = 5.4, |90-79.4| = 10.6, |68-79.4| = 11.4, |75-79.4| = 4.4, and |79-79.4| = 0.4. Finally, we calculate the average of these absolute differences: (5.4+10.6+11.4+4.4+0.4)/5 = 6.48. Therefore, the mean absolute deviation for the set S is 6.48.

Explanation

The mean absolute deviation (MAD) is a measure of the average distance between each data point and the mean of the set. To find the MAD, we first calculate the mean of the set, which is (85+90+68+75+79)/5 = 79.4. Then, we find the absolute difference between each data point and the mean: |85-79.4| = 5.4, |90-79.4| = 10.6, |68-79.4| = 11.4, |75-79.4| = 4.4, and |79-79.4| = 0.4. Finally, we calculate the average of these absolute differences: (5.4+10.6+11.4+4.4+0.4)/5 = 6.48. Therefore, the mean absolute deviation for the set S is 6.48.

3. Find the mean absolute deviation for the set below. S = {65, 90, 85, 70, 70, 95, 55}

12.24

75.7

85.7

40

The mean absolute deviation is a measure of how spread out the data points are from the mean. To find the mean absolute deviation, we first find the mean of the set. The mean of the set {65, 90, 85, 70, 70, 95, 55} is 75.7. Then, we find the absolute value of the difference between each data point and the mean, and calculate the average of these absolute differences. The mean absolute deviation for this set is 12.24.

Explanation

The mean absolute deviation is a measure of how spread out the data points are from the mean. To find the mean absolute deviation, we first find the mean of the set. The mean of the set {65, 90, 85, 70, 70, 95, 55} is 75.7. Then, we find the absolute value of the difference between each data point and the mean, and calculate the average of these absolute differences. The mean absolute deviation for this set is 12.24.

4. Find the mean absolute deviation of the fulfilled items on Sherrie's registry. $29, $58, $15, $129, $75, $22

196

54.7

114

32.67

The mean absolute deviation is a measure of the average distance between each data point and the mean of the data set. To find the mean absolute deviation, we first calculate the mean of the data set, which is the sum of all the numbers divided by the total count. In this case, the mean is (29 + 58 + 15 + 129 + 75 + 22) / 6 = 328 / 6 = 54.67.

Next, we find the absolute deviation for each data point by subtracting the mean from each number and taking the absolute value. The absolute deviations are: |29 - 54.67| = 25.67, |58 - 54.67| = 3.33, |15 - 54.67| = 39.67, |129 - 54.67| = 74.33, |75 - 54.67| = 20.33, |22 - 54.67| = 32.67.

Finally, we calculate the mean of these absolute deviations, which is (25.67 + 3.33 + 39.67 + 74.33 + 20.33 + 32.67) / 6 = 196 / 6 = 32.67. Therefore, the mean absolute deviation of the fulfilled items on Sherrie's registry is 32.67.

Explanation

The mean absolute deviation is a measure of the average distance between each data point and the mean of the data set. To find the mean absolute deviation, we first calculate the mean of the data set, which is the sum of all the numbers divided by the total count. In this case, the mean is (29 + 58 + 15 + 129 + 75 + 22) / 6 = 328 / 6 = 54.67.

Next, we find the absolute deviation for each data point by subtracting the mean from each number and taking the absolute value. The absolute deviations are: |29 - 54.67| = 25.67, |58 - 54.67| = 3.33, |15 - 54.67| = 39.67, |129 - 54.67| = 74.33, |75 - 54.67| = 20.33, |22 - 54.67| = 32.67.

Finally, we calculate the mean of these absolute deviations, which is (25.67 + 3.33 + 39.67 + 74.33 + 20.33 + 32.67) / 6 = 196 / 6 = 32.67. Therefore, the mean absolute deviation of the fulfilled items on Sherrie's registry is 32.67.

5. Family A and Family B both have 8 people in their family. The ages of each member is listed below. Which statement is correct about the variability of the two families. Family A: 35, 5, 42, 9, 16, 3, 8, 12 Family B: 1, 5, 29, 3, 7, 35, 6, 9

The variability for Family A is greater because the mean is greater for Family A.

The variability for Family B is greater because the mean absolute deviation is greater for Family B.

There is not enough information to determine the variability.

The correct answer is that the variability for Family B is greater because the mean absolute deviation is greater for Family B. This can be determined by calculating the mean absolute deviation for both families. The mean absolute deviation measures the average distance between each data point and the mean of the data set. By comparing the mean absolute deviation for both families, we can determine which family has a greater variability.

Explanation

The correct answer is that the variability for Family B is greater because the mean absolute deviation is greater for Family B. This can be determined by calculating the mean absolute deviation for both families. The mean absolute deviation measures the average distance between each data point and the mean of the data set. By comparing the mean absolute deviation for both families, we can determine which family has a greater variability.