5 9
5 2 1 1 6 3 9
5 1 0 7 0 2 3 6 7 8
2 1 8 3
0 9
Key: 9|6 means 69 Key: 5|8 means 58
Calculate the mean of each data set.
Calculate the mean absolute deviation (MAD) of each data set.
Which set is more variable? How do you know?
any thing would work like a link or some thing
Search for "stem and leaf plot".
In results, the sites mathsisfun and purplemath have good info.
To calculate the mean of each dataset, you need to find the average of all the numbers in each set.
Dataset 1: 5, 9
Mean = (5 + 9) / 2 = 14 / 2 = 7
Dataset 2: 5, 2, 1, 1, 6, 3, 9
Mean = (5 + 2 + 1 + 1 + 6 + 3 + 9) / 7 = 27 / 7 ≈ 3.857
Dataset 3: 5, 1, 0, 7, 0, 2, 3, 6, 7, 8
Mean = (5 + 1 + 0 + 7 + 0 + 2 + 3 + 6 + 7 + 8) / 10 = 39 / 10 = 3.9
Dataset 4: 2, 1, 8, 3
Mean = (2 + 1 + 8 + 3) / 4 = 14 / 4 = 3.5
Dataset 5: 0, 9
Mean = (0 + 9) / 2 = 9 / 2 = 4.5
To calculate the Mean Absolute Deviation (MAD) of each dataset, you need to find the average absolute difference between each number and the mean.
Dataset 1:
|5 - 7| + |9 - 7| / 2 = 2 + 2 / 2 = 4 / 2 = 2
Dataset 2:
|5 - 3.857| + |2 - 3.857| + |1 - 3.857| + |1 - 3.857| + |6 - 3.857| + |3 - 3.857| + |9 - 3.857| / 7 ≈ 1.143 + 1.857 + 2.857 + 2.857 + 2.143 + 0.857 + 5.143 / 7 ≈ 0.2 + 0.265 + 0.408 + 0.408 + 0.306 + 0.122 + 0.734 ≈ 2.243
Dataset 3:
|5 - 3.9| + |1 - 3.9| + |0 - 3.9| + |7 - 3.9| + |0 - 3.9| + |2 - 3.9| + |3 - 3.9| + |6 - 3.9| + |7 - 3.9| + |8 - 3.9| / 10 ≈ 1.1 + 2.9 + 3.9 + 3.1 + 3.9 + 1.9 + 0.9 + 2.1 + 3.1 + 4.1 / 10 ≈ 0.11 + 0.29 + 0.39 + 0.31 + 0.39 + 0.19 + 0.09 + 0.21 + 0.31 + 0.41 ≈ 2.3
Dataset 4:
|2 - 3.5| + |1 - 3.5| + |8 - 3.5| + |3 - 3.5| / 4 ≈ 1.5 + 2.5 + 4.5 + 0.5 / 4 ≈ 0.375 + 0.625 + 1.125 + 0.125 ≈ 2.25
Dataset 5:
|0 - 4.5| + |9 - 4.5| / 2 = 4.5 + 4.5 / 2 = 9 / 2 = 4.5
Now, to determine which dataset is more variable, we compare the MADs. The dataset with the larger MAD is considered to be more variable.
In this case, Dataset 2 has the largest MAD of approximately 2.243, while the rest of the datasets have MADs less than 2.243. Therefore, Dataset 2 is the most variable dataset.
You can determine the dataset with the larger MAD by comparing the calculated MADs. The dataset with the larger value is more variable, as it has a greater average absolute difference from the mean.