question archive Calculate the population mean, standard deviation, and skewness of each of the following two series: Series #1 −51 −21 21 51 Series #2 −61 −7 33 35
Calculate the population mean, standard deviation, and skewness of each of the following two series: Series #1 −51 −21 21 51 Series #2 −61 −7 33 35
Subject:MathPrice:9.82 Bought3
Calculate the population mean, standard deviation, and skewness of each of the following two series:
Series #1 −51 −21 21 51
Series #2 −61 −7 33 35
Purchase A New Answer
Custom new solution created by our subject matter experts
GET A QUOTE
Answer Preview
Series 1
Population mean = ∑x/n
Population mean = 0/4 = 0
| x | x - x? | (x - x?)2 | (x - x?)3 |
| -51 | -51 | 2601 | -132651 |
| -21 | -21 | 441 | -9261 |
| 21 | 21 | 441 | 9261 |
| 51 | 51 | 2601 | 132651 |
| Total | 6084 | 0 |
σ = √∑(x - x?)2
σ = √6084/4 = 39
Skewness = ∑(x - x?)3/n(σ3)
Skewness = 0/4(393) = 0
Series 2
Population mean = ∑x/n
Population mean = 0/4 = 0
| x | x - x? | (x - x?)2 | (x - x?)3 |
| -61 | -61 | 3721 | -226981 |
| -7 | -7 | 49 | -343 |
| 33 | 33 | 1089 | 35937 |
| 35 | 35 | 1225 | 42875 |
| Total | 6084 | -148512 |
σ = √∑(x - x?)2
σ = √6084/4 = 39
Skewness = ∑(x - x?)3/n(σ3)
Skewness = -148512/4(393) =-0.6259
Step-by-step explanation
eries 1
Population mean = ∑x/n
Population mean = 0/4 = 0
| x | x - x? | (x - x?)2 | (x - x?)3 |
| -51 | -51 | 2601 | -132651 |
| -21 | -21 | 441 | -9261 |
| 21 | 21 | 441 | 9261 |
| 51 | 51 | 2601 | 132651 |
| Total | 6084 | 0 |
σ = √∑(x - x?)2
σ = √6084/4 = 39
Skewness = ∑(x - x?)3/n(σ3)
Skewness = 0/4(393) = 0
Series 2
Population mean = ∑x/n
Population mean = 0/4 = 0
| x | x - x? | (x - x?)2 | (x - x?)3 |
| -61 | -61 | 3721 | -226981 |
| -7 | -7 | 49 | -343 |
| 33 | 33 | 1089 | 35937 |
| 35 | 35 | 1225 | 42875 |
| Total | 6084 | -148512 |
σ = √∑(x - x?)2
σ = √6084/4 = 39
Skewness = ∑(x - x?)3/n(σ3)
Skewness = -148512/4(393) =-0.6259
