Question

The list shows the heights of 6 students in inches. 63, 70, 68, 73, 58, 67 What is the mean absolute deviation for these numbers?

Answer 1

To find the mean absolute deviation (MAD) for a set of numbers, calculate the average difference between each number and the mean. For the given set of heights, the MAD is approximately 3.83 inches.

Step-by-step explanation:

To find the mean absolute deviation (MAD) for a set of numbers, we need to follow these steps:

1. Find the mean of the numbers by adding them up and dividing by the total count.
2. Subtract the mean from each individual number to get the deviation.
3. Take the absolute value of each deviation.
4. Add up all the absolute deviations.
5. Divide the sum of the absolute deviations by the total count of numbers to get the mean absolute deviation.

Let's calculate the MAD for the given set of heights: 63, 70, 68, 73, 58, 67.

1. Add up all the heights: 63 + 70 + 68 + 73 + 58 + 67 = 399.
2. Find the mean: 399 / 6 = 66.5.
3. Calculate the deviations: 63 - 66.5 = -3.5, 70 - 66.5 = 3.5, 68 - 66.5 = 1.5, 73 - 66.5 = 6.5, 58 - 66.5 = -8.5, 67 - 66.5 = 0.5.
4. Take the absolute value of each deviation: |-3.5| = 3.5, |3.5| = 3.5, |1.5| = 1.5, |6.5| = 6.5, |-8.5| = 8.5, |0.5| = 0.5.
5. Add up all the absolute deviations: 3.5 + 3.5 + 1.5 + 6.5 + 8.5 + 0.5 = 23.
6. Divide the sum by the total count: 23 / 6 = 3.83 (rounded to two decimal places).

Therefore, the mean absolute deviation for the given set of heights is approximately 3.83 inches.

Answer 2

Answer with Step-by-step explanation:

Mean absolute deviation means mean of the absolute deviation around mean

so, first we calculate the mean

Mean= sum of all observations/total number of observations

= (63+70+68+73+58+67)/6

=66.5

Absolute deviations around mean:

|63-66.5|=3.5

|70-66.5|=3.5

|68-66.5|=1.5

|73-66.5|=6.5

|58-66.5|=8.5

|67-66.5|=0.5

Mean of absolute deviation around mean=(3.5+3.5+1.5+6.5+8.5+0.5)/6

= 4

Hence, mean absolute deviation is:

4