Question
Download Solution PDFWhat is the sum of deviations of the variate values 73, 85, 92, 105, 120 from their mean?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
For the observations \(\rm x_1 ,x_2 ,x_3 ,..........,x_n\)
Mean (\(\rm\overline x\)) = \(\rm {x_1 +x_2 + x_3 +..........+x_n\over n}\)
Deviation of the observation from the mean = xi - \(\rm\overline x\)
where i ∈ [1, n]
Calculation:
Mean = \(\rm {73+85+92+105+120\over 5}\)
\(\rm\overline x\) = \(\rm {475\over 5}\) = 95
| Value | Mean | Deviation of the value |
| 73 | 95 | 73 - 95 = -22 |
| 85 | 95 | 85 - 95 = -10 |
| 92 | 95 | 92 - 95 = -3 |
| 105 | 95 | 105 - 95 = 10 |
| 120 | 95 | 120 - 95 = 25 |
The sum of the deviation = -22 +(-10) + (-3) + 10 + 25 = 0
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