What is the sum of the absolute deviations in the following dataset: 68, 51, 75, 78, 94, 35?
To find the sum of the absolute deviations, we first need to find the mean of the dataset.
Mean = (68 + 51 + 75 + 78 + 94 + 35) / 6 = 401 / 6 = 66.83 (rounded to two decimal places)
Now, we calculate the absolute deviation for each value in the dataset by subtracting the mean from the value and taking the absolute value.
Absolute deviation for 68 = |68 - 66.83| = 1.17
Absolute deviation for 51 = |51 - 66.83| = 15.83
Absolute deviation for 75 = |75 - 66.83| = 8.17
Absolute deviation for 78 = |78 - 66.83| = 11.17
Absolute deviation for 94 = |94 - 66.83| = 27.17
Absolute deviation for 35 = |35 - 66.83| = 31.83
Finally, we sum up these absolute deviations.
Sum of absolute deviations = 1.17 + 15.83 + 8.17 + 11.17 + 27.17 + 31.83 = 95.34
Therefore, the sum of the absolute deviations in the dataset is 95.34.
To find the sum of the absolute deviations in a dataset, follow these steps:
Step 1: Calculate the mean of the dataset.
To do this, add up all of the numbers in the dataset and divide by the total number of values.
68 + 51 + 75 + 78 + 94 + 35 = 401
The mean is 401 divided by 6, which equals 66.83 (rounded to two decimal places).
Step 2: Find the absolute deviation for each value.
To do this, subtract the mean from each individual value and take the absolute value of the result.
For example, for the first value of 68:
|68 - 66.83| = 1.17 (rounded to two decimal places).
Step 3: Find the sum of all the absolute deviations.
Add up all the absolute deviations calculated in step 2.
1.17 + |51 - 66.83| + |75 - 66.83| + |78 - 66.83| + |94 - 66.83| + |35 - 66.83|
Step 4: Calculate the final sum.
Add up all the absolute deviations calculated in step 3.
1.17 + 15.83 + 8.17 + 11.17 + 27.17 + 31.83 = 95.34 (rounded to two decimal places).
Therefore, the sum of the absolute deviations in the given dataset is 95.34.