The top five test scores in Mr. Rhodes class were: 98, 92, 96, 97, and 97. What is the mean absolute deviation?
mean = (1/5) ( 98+92+96+97+97) = 480/5 = 96
mean abs deviation = (1/5)[ |98-96 |+|92-96| .....
=(1/5)( 2+4+0+1+1)
= 8/5
Well, Mr. Rhodes clearly knows how to teach, but let me do the math for you. To find the mean absolute deviation, we need to calculate the average of each score's absolute deviation from the mean.
First, let's find the mean of those test scores: (98 + 92 + 96 + 97 + 97) / 5 = 96
Now, let's calculate the absolute deviation for each score:
|98 - 96| = 2
|92 - 96| = 4
|96 - 96| = 0
|97 - 96| = 1
|97 - 96| = 1
Next, we find the average of these absolute deviations: (2 + 4 + 0 + 1 + 1) / 5 = 8 / 5 = 1.6
So, the mean absolute deviation of Mr. Rhodes' test scores is about 1.6. Keep up the good work, Mr. Rhodes!
To find the mean absolute deviation, follow these steps:
Step 1: Find the mean (average) of the data set.
To find the mean, sum up all the values and divide by the total number of values:
Mean = (98 + 92 + 96 + 97 + 97) / 5 = 480 / 5 = 96
Step 2: Find the deviation for each data point.
To find the deviation, subtract each data point from the mean:
Deviation for 98 = 98 - 96 = 2
Deviation for 92 = 92 - 96 = -4
Deviation for 96 = 96 - 96 = 0
Deviation for 97 = 97 - 96 = 1
Deviation for 97 = 97 - 96 = 1
Step 3: Find the absolute value of each deviation.
To find the absolute value, ignore the positive or negative sign (if any):
|2| = 2
|-4| = 4
|0| = 0
|1| = 1
|1| = 1
Step 4: Find the average of the absolute deviations.
To find the mean absolute deviation, sum up all the absolute deviations and divide by the total number of values:
Mean Absolute Deviation = (2 + 4 + 0 + 1 + 1) / 5 = 8 / 5 = 1.6
Therefore, the mean absolute deviation is 1.6.
To find the mean absolute deviation, follow these steps:
Step 1: Calculate the mean (average) of the test scores.
To find the mean, add up all the test scores and divide the sum by the number of scores:
Mean = (98 + 92 + 96 + 97 + 97) / 5 = 480 / 5 = 96.
Step 2: Calculate the deviation for each test score.
Subtract the mean from each test score to find the deviation from the mean:
Deviation for 98 = 98 - 96 = 2
Deviation for 92 = 92 - 96 = -4
Deviation for 96 = 96 - 96 = 0
Deviation for 97 = 97 - 96 = 1
Deviation for 97 = 97 - 96 = 1
Step 3: Calculate the absolute value of each deviation.
Since mean absolute deviation requires absolute values, we ignore the negative signs:
Absolute deviation for 98 = |2| = 2
Absolute deviation for 92 = |-4| = 4
Absolute deviation for 96 = |0| = 0
Absolute deviation for 97 = |1| = 1
Absolute deviation for 97 = |1| = 1
Step 4: Calculate the mean of the absolute deviations.
To find the mean of the absolute deviations, add up all the absolute deviations and divide the sum by the number of scores:
Mean absolute deviation = (2 + 4 + 0 + 1 + 1) / 5 = 8 / 5 = 1.6.
Therefore, the mean absolute deviation of the test scores is 1.6.