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?

Question 15 options:

24


66.5


4


67.5

Answer 1

To calculate the mean absolute deviation (MAD) of the heights of the students, we follow these steps:

1. Calculate the mean (average) of the numbers.
2. Find the absolute deviations from the mean.
3. Calculate the mean of those absolute deviations.

**Step 1: Calculate the mean**

Given heights: 63, 70, 68, 73, 58, 67

Sum of heights = 63 + 70 + 68 + 73 + 58 + 67 = 399

Number of students = 6

Mean = Total Sum / Number of Students = 399 / 6 = 66.5

**Step 2: Find the absolute deviations from the mean**

Absolute Deviations:

- |63 - 66.5| = | -3.5 | = 3.5
- |70 - 66.5| = | 3.5 | = 3.5
- |68 - 66.5| = | 1.5 | = 1.5
- |73 - 66.5| = | 6.5 | = 6.5
- |58 - 66.5| = | -8.5 | = 8.5
- |67 - 66.5| = | 0.5 | = 0.5

**Step 3: Calculate the mean of the absolute deviations**

Sum of absolute deviations = 3.5 + 3.5 + 1.5 + 6.5 + 8.5 + 0.5 = 24

Mean Absolute Deviation = Total Absolute Deviations / Number of Students = 24 / 6 = 4

Therefore, the mean absolute deviation is **4**.

So the correct answer is:

**4**