Leon counts the number of bugs he finds on his tomato plants each day and collects the following data: 18, 24, 15, 9, 10. The mean is 15.2. What is the final equation that he would use in determining the mean absolute deviation? Round each value to the nearest tenth.(2 points)
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To determine the mean absolute deviation, Leon would use the equation:
∑ |x - mean| ÷ n = mean absolute deviation
Leon counts the number of bugs he finds on his tomato plants each day and collects the following data: 18, 24, 15, 9, 10. The mean is 15.2. What is the final equation that he would use in determining the mean absolute deviation? Round each value to the nearest tenth.(2 points)
To determine the mean absolute deviation, Leon would use the equation:
∑ |x - mean| ÷ n = mean absolute deviation
Leon counts the number of bugs he finds on his tomato plants each day and collects the following data: 18, 24, 15, 9, 10. The mean is 15.2. What is the final equation that he would use in determining the mean absolute deviation? Round each value to the nearest tenth.(2 points).
To determine the mean absolute deviation, Leon would use the equation:
∑ |x - mean| ÷ n = mean absolute deviation
For the given data, the equation would be:
(|18 - 15.2| + |24 - 15.2| + |15 - 15.2| + |9 - 15.2| + |10 - 15.2|) ÷ 5 = mean absolute deviation
To calculate the mean absolute deviation, Leon would use the following equation:
Mean Absolute Deviation = Σ(|x - mean|) ÷ n
Where:
- Σ signifies the sum of all the absolute differences between each individual data point (x) and the mean,
- |x - mean| represents the absolute value of the difference between each data point and the mean,
- n is the total number of data points.
In this case, the data points are: 18, 24, 15, 9, 10.
The mean is given as 15.2.
To calculate the mean absolute deviation, we need to find the absolute difference between each data point and the mean, then sum up all these differences and divide by the total number of data points.
Step-by-step computation:
|18 - 15.2| + |24 - 15.2| + |15 - 15.2| + |9 - 15.2| + |10 - 15.2|
= 2.8 + 8.8 + 0.2 + 6.2 + 5.2
= 23.2
Therefore, the final equation for determining the mean absolute deviation is:
Mean Absolute Deviation = 23.2 ÷ 5
To determine the mean absolute deviation (MAD) for the given data set, we need to calculate the absolute difference between each value in the data set and the mean, and then take the average of these absolute differences.
First, we calculate the absolute difference between each value and the mean:
|18 - 15.2| = 2.8
|24 - 15.2| = 8.8
|15 - 15.2| = 0.2
|9 - 15.2| = 6.2
|10 - 15.2| = 5.2
Next, we calculate the average of these absolute differences:
(2.8 + 8.8 + 0.2 + 6.2 + 5.2) ÷ 5 = 5.64
Therefore, the final equation that Leon would use to determine the mean absolute deviation is:
MAD = 5.64