The number of words Mr. Ahmad’s students read per minute is 109, 89, 112, 98, 101, 105, 120, 106. What is the mean absolute deviation of the dataset? Round the answer to the nearest tenth.
To find the mean absolute deviation (MAD), follow these steps:
Step 1: Calculate the mean (average) of the dataset.
Add up all the numbers in the dataset and divide the sum by the number of values.
109 + 89 + 112 + 98 + 101 + 105 + 120 + 106 = 840
840 / 8 = 105
Step 2: Calculate the absolute deviations from the mean for each value.
Find the absolute value of the difference between each value in the dataset and the mean.
|109 - 105| = 4
|89 - 105| = 16
|112 - 105| = 7
|98 - 105| = 7
|101 - 105| = 4
|105 - 105| = 0
|120 - 105| = 15
|106 - 105| = 1
Step 3: Calculate the average of the absolute deviations.
Add up all the absolute deviations and divide the sum by the number of values.
4 + 16 + 7 + 7 + 4 + 0 + 15 + 1 = 54
54 / 8 = 6.75
Therefore, the mean absolute deviation of the dataset is approximately 6.8 when rounded to the nearest tenth.
To find the mean absolute deviation (MAD) of a dataset, follow these steps:
1. Calculate the mean (average) of the dataset by summing all the values and dividing by the total number of values.
So, for the given dataset: 109 + 89 + 112 + 98 + 101 + 105 + 120 + 106 = 840
The total number of values is 8, so the mean would be 840 / 8 = 105.
2. Find the absolute deviation of each value from the mean by subtracting the mean from each value and taking the absolute value.
The absolute deviations for each value in the dataset would be:
|109 - 105| = 4
|89 - 105| = 16
|112 - 105| = 7
|98 - 105| = 7
|101 - 105| = 4
|105 - 105| = 0
|120 - 105| = 15
|106 - 105| = 1
3. Calculate the average of these absolute deviations to get the mean absolute deviation (MAD).
The sum of the absolute deviations is 4 + 16 + 7 + 7 + 4 + 0 + 15 + 1 = 54.
Since there are 8 values, the MAD would be 54 / 8 = 6.75.
Therefore, the mean absolute deviation (MAD) of the dataset is 6.8 (rounded to the nearest tenth).
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 find the mean absolute deviation, we first need to find the mean of the dataset:
Mean = (109+89+112+98+101+105+120+106)/8 = 103.5
Next, we find the deviation of each data point from the mean:
|109 - 103.5| = 5.5
|89 - 103.5| = 14.5
|112 - 103.5| = 8.5
|98 - 103.5| = 5.5
|101 - 103.5| = 2.5
|105 - 103.5| = 1.5
|120 - 103.5| = 16.5
|106 - 103.5| = 2.5
To find the mean absolute deviation, we add up all the deviations and divide by the number of data points:
Mean absolute deviation = (5.5+14.5+8.5+5.5+2.5+1.5+16.5+2.5)/8 = 6.875
Rounded to the nearest tenth, the mean absolute deviation is 6.9. Therefore, the answer is 6.9.