Question

Find the mean of the following Data set {72, 73, 55, 67, 80, 73, 77, 63, 67} Round to the nearest hundredth if necessary
Mean = __

Find the deviation of each data point from the mean for the following data set: {72, 73, 55, 67, 80, 73, 77, 63, 67}

Find the average deviation of the data set {72, 73, 55, 67, 80, 73, 77, 63, 67}. Round to the nearest hundredth if necessary.
Average deviation = __
THE ANSWERS LISTED BELOW ARE WRONG AND NEED EDITED.
Mean = 69.67
- 72: 72 − 69.67 = 2.33
- 73: 73 − 69.67 = 3.33
- 55: 55 − 69.67 = −14.67
- 67: 67 − 69.67 = −2.67
- 80: 80 − 69.67 = 10.33
- 73: 73 − 69.67 = 3.33
- 77: 77 − 69.67 = 7.33
- 63: 63 − 69.67 = −6.67
- 67: 67 − 69.67 = −2.67
5.93

Answer 1

Your listed answers are actually correct. Work shown:

1) Mean
Sum = 72+73+55+67+80+73+77+63+67 = 627
Mean = 627/9 = 69.666666... = 69.67 (rounded to the nearest hundredth)

2) Deviations (xi − mean), rounded to 2 decimals
- 72: 72 − 69.666... = 2.33
- 73: 73 − 69.666... = 3.33
- 55: 55 − 69.666... = −14.67
- 67: 67 − 69.666... = −2.67
- 80: 80 − 69.666... = 10.33
- 73: 73 − 69.666... = 3.33
- 77: 77 − 69.666... = 7.33
- 63: 63 − 69.666... = −6.67
- 67: 67 − 69.666... = −2.67

(Exact mean = 209/3, deviations = (3·x − 209)/3.)

3) Average deviation (mean absolute deviation)
Sum of absolute deviations = 160/3 ≈ 53.3333
Average = (160/3)/9 = 160/27 ≈ 5.9259 → 5.93 (rounded to the nearest hundredth)

Final answers:
Mean = 69.67
Deviations listed above
Average deviation = 5.93