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) _ ÷ _ = _ fill in these blanks for the answer
To find the mean absolute deviation, Leon would use the equation:
Σ|Xi - μ| / n = MAD
where Σ refers to the sum of the absolute differences between each data point (Xi) and the mean (μ), divided by the total number of data points (n).
In this case, the values to fill in the blanks would be:
Σ|Xi - 15.2| / 5 = MAD
( |18 - 15.2| + |24 - 15.2| + |15 - 15.2| + |9 - 15.2| + |10 - 15.2| ) / 5 = MAD
(2.8 + 8.8 + 0.2 + 6.2 + 5.2) / 5 = MAD
23.2 / 5 = MAD
4.6 = MAD
Therefore, the final equation that Leon would use to determine the mean absolute deviation is:
Σ|Xi - 15.2| / 5 = 4.6
i did not understand that
I apologize for the confusion. Let me simplify it for you:
To find the mean absolute deviation (MAD), the formula Leon would use is:
MAD = Σ|Xi - μ| / n
Where:
- Σ is the sum of the absolute differences between each data point (Xi) and the mean (μ)
- n is the total number of data points
Given the data Leon collected and the mean (15.2), we need to find the absolute differences between each data point 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
Now, add up these absolute differences:
2.8 + 8.8 + 0.2 + 6.2 + 5.2 = 23.2
Finally, divide the sum of the absolute differences by the total number of data points (5) to get the MAD:
MAD = 23.2 / 5
MAD = 4.6
Therefore, the mean absolute deviation that Leon would use is 4.6.