The table shows the heights of 5 students in inches.What is the mean absolute deviation for these numbers? show your steps.
59, 71, 68, 75, 67
To find the mean absolute deviation, you need to first find the mean of the data set.
1. Add up all the numbers:
59 + 71 + 68 + 75 + 67 = 340
2. Divide by the total number of values:
340 ÷ 5 = 68
The mean of the data set is 68 inches.
Next, find the absolute deviation for each value by subtracting the mean from each individual value:
|59 - 68| = 9
|71 - 68| = 3
|68 - 68| = 0
|75 - 68| = 7
|67 - 68| = 1
Then, find the mean of the absolute deviations by adding them up and dividing by the number of values:
(9 + 3 + 0 + 7 + 1) ÷ 5 = 20 ÷ 5 = 4
Therefore, the mean absolute deviation for this set of data is 4 inches.
To find the mean absolute deviation (MAD) for a set of numbers, you need to follow these steps:
Step 1: Calculate the mean (average) of the dataset.
Step 2: Subtract the mean from each individual data point to find the deviation from the mean.
Step 3: Take the absolute value of each deviation.
Step 4: Find the average of the absolute deviations to obtain the MAD.
Let's go through the steps to find the MAD for the given dataset:
Step 1: Calculate the mean
To find the mean, add up all the individual numbers (heights) and divide the sum by the total number of values.
59 + 71 + 68 + 75 + 67 = 340
340 ÷ 5 = 68
So, the mean (average) of the dataset is 68 inches.
Step 2: Find the deviation from the mean for each data point
Subtract the mean (68) from each individual height to find the deviation from the mean:
59 - 68 = -9
71 - 68 = 3
68 - 68 = 0
75 - 68 = 7
67 - 68 = -1
The deviations from the mean are: -9, 3, 0, 7, -1.
Step 3: Take the absolute value of each deviation
The absolute value of a number is its distance from zero on the number line. It is always positive.
| -9 | = 9
| 3 | = 3
| 0 | = 0
| 7 | = 7
| -1 | = 1
The absolute deviations from the mean are: 9, 3, 0, 7, 1.
Step 4: Find the average of the absolute deviations
To find the MAD, add up all the absolute deviations and divide the sum by the total number of values (in this case, 5).
9 + 3 + 0 + 7 + 1 = 20
20 ÷ 5 = 4
Hence, the mean absolute deviation (MAD) for the given dataset is 4 inches.
To find the mean absolute deviation for a set of numbers, follow these steps:
Step 1: Calculate the mean (average) of the numbers.
To calculate the mean, add up all the numbers and divide the sum by the total count.
59 + 71 + 68 + 75 + 67 = 340
340 ÷ 5 = 68
The mean height is 68 inches.
Step 2: Calculate the deviation for each number.
To calculate the deviation, subtract the mean from each number.
59 - 68 = -9
71 - 68 = 3
68 - 68 = 0
75 - 68 = 7
67 - 68 = -1
The deviations are: -9, 3, 0, 7, -1.
Step 3: Find the absolute value of each deviation.
To find the absolute value, ignore the negative signs if any.
|-9| = 9
|3| = 3
|0| = 0
|7| = 7
|-1| = 1
The absolute deviations are: 9, 3, 0, 7, 1.
Step 4: calculate the mean absolute deviation.
To calculate the mean absolute deviation, find the average of the absolute deviations.
9 + 3 + 0 + 7 + 1 = 20
20 ÷ 5 = 4
The mean absolute deviation is 4 inches.