8 Elizabeth recorded the length in centimeters of the
pinky fingers of 10 students in her math class.
The results are shown below. What is the mean
absolute deviation for length of a pinky finger? 6.1,
5.4, 5.8, 6.3, 6.2, 5.9, 6.5, 5.2, 4.9, 5.5
Sal Khan does an excellent job of this topic in this video.
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-data-statistics/cc-6-mad/v/mean-absolute-deviation
He goes through two different cases
i dont know i need help myself im a 8th grader looking for help
To find the mean absolute deviation (MAD), you need to follow these steps:
Step 1: Find the mean (average) of the data set.
Step 2: Calculate the absolute difference between each data point and the mean.
Step 3: Find the average of these absolute differences to get the MAD.
Let's calculate the MAD for the given data set:
Step 1: Find the mean
Add up all the values: 6.1 + 5.4 + 5.8 + 6.3 + 6.2 + 5.9 + 6.5 + 5.2 + 4.9 + 5.5 = 57.8
Divide the sum by the number of values (10): 57.8 / 10 = 5.78
Step 2: Calculate the absolute difference
For each value, subtract the mean and take the absolute value:
|6.1 - 5.78| = 0.32
|5.4 - 5.78| = 0.38
|5.8 - 5.78| = 0.02
|6.3 - 5.78| = 0.52
|6.2 - 5.78| = 0.42
|5.9 - 5.78| = 0.12
|6.5 - 5.78| = 0.72
|5.2 - 5.78| = 0.58
|4.9 - 5.78| = 0.88
|5.5 - 5.78| = 0.28
Step 3: Find the average of the absolute differences
Add up all the absolute differences and divide by the number of values (10):
(0.32 + 0.38 + 0.02 + 0.52 + 0.42 + 0.12 + 0.72 + 0.58 + 0.88 + 0.28) / 10 = 0.344
Therefore, the mean absolute deviation for the length of a pinky finger is approximately 0.344 centimeters.
To find the mean absolute deviation (MAD), follow these steps:
Step 1: Find the mean (average) of the data set.
To do this, add up all the values and divide by the total number of values.
In this case, add up all the lengths: 6.1 + 5.4 + 5.8 + 6.3 + 6.2 + 5.9 + 6.5 + 5.2 + 4.9 + 5.5 = 57.8
Then divide the sum by the total number of values, which in this case is 10: 57.8 / 10 = 5.78
Step 2: Find the absolute deviations for each value.
To do this, subtract the mean from each value. Taking the first value as an example: 6.1 - 5.78 = 0.32
Repeat this process for each value and calculate the absolute deviations:
0.32, -0.38, 0.02, 0.52, 0.42, 0.12, 0.72, -0.58, -0.88, -0.28
Step 3: Find the mean of the absolute deviations.
Add up all the absolute deviations and divide by the total number of values.
Adding up the absolute deviations: 0.32 + (-0.38) + 0.02 + 0.52 + 0.42 + 0.12 + 0.72 + (-0.58) + (-0.88) + (-0.28) = -0.74
Then divide by the total number of values, which is 10: -0.74 / 10 = -0.074
Step 4: Find the absolute value of the mean of the absolute deviations.
Since the mean of the absolute deviations can be negative, we need to take the absolute value to get the MAD.
In this case, the absolute value of -0.074 is 0.074.
Therefore, the mean absolute deviation for the length of a pinky finger is 0.074 centimeters.