Question
What is the sum of the absolute deviations in the following dataset: 68, 51, 75, 78, 94, 35?
Answers
GPT 3.5
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.
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.