Question

Serge had the following scores on his math tests last quarter: 100, 94, 78, 88, 87, 93, 96, and 92. Find the mean absolute deviation for the set of data. Round to the nearest tenth. How many data values are closer than one mean absolute deviation away from the mean?

(a) 6.4; 5 values

(b) 8.4; 6 values

(c) 10.4; 7 values

(d) 12.4; 8 values

Answer 1

To find the mean absolute deviation, find the mean, subtract it from each value, take the absolute value, add them up and divide by the number of values. There are 5 values closer than one mean absolute deviation away from the mean.

Step-by-step explanation:

To find the mean absolute deviation (MAD) for a set of data, we need to:

1. Find the mean of the data set by adding up all the numbers and dividing the sum by the total number of values.
2. Subtract the mean from each value in the data set to find the differences.
3. Take the absolute value (positive value) of each difference.
4. Add up all the absolute differences and divide the sum by the total number of values to find the MAD.

For the given data set, the mean is 91.625. The absolute differences are: 8.375, 3.625, 12.625, 2.625, 3.625, 1.625, 4.625, and 1.625. The sum of the absolute differences is 39.75. Dividing this sum by the total number of values (8), we get a MAD of 4.96875, rounded to the nearest tenth.

To determine how many data values are closer than one MAD away from the mean, we need to count the number of values that have an absolute difference less than or equal to the MAD. In this case, there are 5 values that meet this condition.