Module 3 SLP Math 201

Module 3 SLP Math 201
Name
Course
Instructor
Date
Data from Module 1
DayMinutes1352383494325406377388349451031 The data represents the time spent driving in the weekdays from home to work in the morning sessions and from work heading home during the evening to night sessions.
Frequency distribution for the data collected
35, 38, 49, 32, 40, 37, 38, 34, 45, and 31
CumulativeCumulativeTime DrivingFrequency Frequency PercentagePercentage31111010321210203413103035141040371510503827207040181080451910904911010100
Standard deviation and variance
DayMinutes (m)M-X(m-x)^2135-2.98.412380.10.0134911.1123.21432-5.934.815402.14.41637-0.90.817380.10.01834-3.915.219457.150.411031-6.947.61Total379284.9Sample Standard Deviation, s5.63Variance (Sample Standard), s231.66Population Standard Deviation, σ
5.34
Variance (Population Standard), σ2
28.49
Total Numbers, N
10
Sum:
379
Mean (Average)
37.9
The population standard deviation is 5.34 being the square root of 28.49 (284.9/10), with the variance the same as the standard deviation squared. However, the sample variance is 31.66 being 284.9/9 and the standard deviation is the square root of 31.65. The differences between the two arises since the sample size is small (n<30), and hence the sample variance is the sum of squared deviation divided by n-1. Typically, as the sample size increases the variance tends to get lower with more estimates. It is also easier to identify the odd observations when there is a larger sample as estimates provide a clearer picture on time spent driving.
Normal distribution
This is not a normal distribution since the mode, mean and median are different, and the computation of the standard deviation, variance and mean makes it easier to understand the distribution. In normally distributed data there is perfect symmetry since the mean mode and median are the same (Black, 2010). The median is 37.5, the mean is 37.9 while the mode is 38, and the skewed normal distribution has a slight positive skew. Even though, the typical relationship in positively skewed distribution is that the mean is the last followed by the median and the mode being the highest of three ther...