The list shows the number of songs that five students each downloaded last week.
32, 43, 38, 28, 51
What is the mean absolute deviation of the numbers in the list?
Responses
A 6.886.88
B 25.625.6
C 128128
D 12.8
To find the mean absolute deviation, you need to find the average of the distances between each data point and the mean.
First, find the mean by summing all the numbers and dividing by the number of students: (32 + 43 + 38 + 28 + 51) / 5 = 192 / 5 = 38.4
Next, find the deviation of each data point from the mean:
|32 - 38.4| = 6.4
|43 - 38.4| = 4.6
|38 - 38.4| = 0.4
|28 - 38.4| = 10.4
|51 - 38.4| = 12.6
Find the mean of these deviations: (6.4 + 4.6 + 0.4 + 10.4 + 12.6) / 5 = 34.4 / 5 = 6.88
So, the mean absolute deviation is 6.88.
The correct answer is A) 6.88.
To find the mean absolute deviation (MAD), follow these steps:
Step 1: Find the mean (average) of the numbers in the list. Add up all the numbers and divide by the total number of values.
(32 + 43 + 38 + 28 + 51) / 5 = 192 / 5 = 38.4
Step 2: Subtract the mean from each number in the list and find the absolute value (the distance from the mean).
|32 - 38.4| = 6.4
|43 - 38.4| = 4.6
|38 - 38.4| = 0.4
|28 - 38.4| = 10.4
|51 - 38.4| = 12.6
Step 3: Find the mean of these absolute values.
(6.4 + 4.6 + 0.4 + 10.4 + 12.6) / 5 = 34 / 5 = 6.8
Therefore, the mean absolute deviation (MAD) of the numbers in the list is 6.8.
The correct answer is A) 6.8.
To find the mean absolute deviation (MAD) of a set of numbers, you need to follow these steps:
1. Find the mean (average) of the numbers in the list. In this case, you would add up all the numbers and divide by the total number of students (which is 5).
Mean = (32 + 43 + 38 + 28 + 51) / 5 = 192 / 5 = 38.4
The mean is 38.4.
2. Subtract the mean from each number in the list to find the deviation. The deviation is the distance between each number and the mean.
Deviation = |number - mean|
For example, the deviation for 32 would be |32 - 38.4| = 6.4.
3. Find the absolute value of each deviation. Absolute value means ignoring any negative signs and considering the positive value only. For example, the absolute value of -6.4 is 6.4.
4. Find the average of the absolute deviations by adding up all the absolute deviations and dividing by the total number of numbers in the list.
Absolute Deviations = (|32 - 38.4| + |43 - 38.4| + |38 - 38.4| + |28 - 38.4| + |51 - 38.4|) / 5
= (6.4 + 4.6 + 0.4 + 10.4 + 12.6) / 5
= 34.4 / 5
= 6.88
So, the mean absolute deviation (MAD) of the numbers in the list is approximately 6.88.
Therefore, the correct answer is A) 6.88