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.(1 point).
To find the mean absolute deviation (MAD), we first need to find the mean of the dataset.
The mean is calculated by adding up all the values and dividing by the number of values.
109 + 89 + 112 + 98 + 101 + 105 + 120 + 106 = 840
Next, we divide the sum by the number of values.
840 ÷ 8 = 105
So, the mean of the dataset is 105.
To find the absolute deviation, we subtract the mean from each value in the dataset and take the absolute value.
Abs(109 - 105) = 4
Abs(89 - 105) = 16
Abs(112 - 105) = 7
Abs(98 - 105) = 7
Abs(101 - 105) = 4
Abs(105 - 105) = 0
Abs(120 - 105) = 15
Abs(106 - 105) = 1
Next, we find the sum of all the absolute deviations.
4 + 16 + 7 + 7 + 4 + 0 + 15 + 1 = 54
The mean absolute deviation is found by dividing the sum of the absolute deviations by the number of values.
54 ÷ 8 ≈ 6.8
Therefore, the mean absolute deviation of the dataset is approximately 6.8.
To find the mean absolute deviation (MAD) of a data set, follow these steps:
Step 1: Find the mean of the dataset.
Step 2: Find the difference between each data point and the mean.
Step 3: Find the absolute value of each difference.
Step 4: Find the mean of the absolute differences.
Let's calculate the mean absolute deviation step by step.
Step 1: Calculate the mean of the dataset.
Total = 109 + 89 + 112 + 98 + 101 + 105 + 120 + 106 = 840
Mean = Total / Number of data points = 840 / 8 = 105
Step 2: Find the difference between each data point 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: Find the absolute value of each difference.
|4| = 4
|-16| = 16
|7| = 7
|-7| = 7
|-4| = 4
|0| = 0
|15| = 15
|1| = 1
Step 4: Find the mean of the absolute differences.
Total of absolute differences = 4 + 16 + 7 + 7 + 4 + 0 + 15 + 1 = 54
MAD = Total of absolute differences / Number of data points = 54 / 8 = 6.75
Therefore, the mean absolute deviation (MAD) of the dataset is approximately 6.8 (rounded to the nearest tenth).