NEWS & EVENTS
Support Molly Johnson!
Our friend Molly was in a pretty rough accident at the Marymoor Velodrome. She is a true steward tot he sport of cyling and will have a long recovery from Hairline fracture on skull which resulted in bruising on other side, broken clavicle which resulted in surgery, 6 fractured ribs and collapsed lung.
She is an athlete and will recover. per her last post she is scheduled to go home today. If you are in a position to help, please do.
http://www.jlvelo.com/page.HelpingMolly.html
Posted June 9, 2013 8:16 AM Pacific Time
Based on Shannons Statistics report WB customers ride an average of 7.3 and 10.1 hours a week.
Woodinville Bicycle
Customer Weekly Riding Times
Shannon Leigh Kehoe
BIS 315
Statistical Problem: How many hours do Woodinville Bicycle customers ride their bikes each week?
Raw Data: Data was gathered by convenience sampling. Customers were asked, at random, how many hours they estimate that they ride each week. Answers are compiled below.
1 1 1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 6 6 6 6 7 7 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 15 15 15 15 16 16 17 18 18 19 19 20 20 25
Analysis #1: Mean/Median/Mode
o Mean: (Sum of all data)/(Number of data points(n))
§ 1+1+…+25= 927
§ n=100
§ 927/100=9.27
§ Mean= 9.27 hrs/wk ridden by WB customers.
o Median: The median number is the middle number from an ordered list of data points. In this case, the number of data points is even, so the median is halfway between the two middle numbers of the list.
§ Data point 50 is 10, data point 51 is also 10.
§ The median of the data points is 10 hrs/wk.
o Mode: The mode represents which number appears most frequently in the data set. In this case, more people answered that they ride 10 hrs/wk than any other number of hours.
§ The mode of the data set is 10 hrs/wk.
Analysis #2: Percentiles
o We want to know how many hours per week one third (33%) of WB customers ride.
§ To find the middle 33% we must first find the lower and upper 33 percentiles.
§ mean)/=z-score (where n is the number of data points and is the standard deviation. Use the standard deviation function on your calculator to determine the data sets σ: 4.8635)
§ Rearrange to solve for the data value: z-score x + mean
§ Using the z-score sheet, find the z-score that correlates to the percentiles we want to work with. 33%=-.44, 66%=0.41.
§ Plug in these numbers into the rearranged equation we worked out above. -0.44 x 4.8635 + 9.27= 7.13. This tells us that 33% of WB riders ride fewer than 7.13 hrs/wk. 0.41 x 4.8635 + 9.27= 11.26. This tells us that 66% of riders rider fewer than 11.26 hrs/wk.
§ The middle 33% ride between the two given numbers, so we can say that a third of WB cyclists ride between 7.13 and 11.26 hrs/wk.
Analysis #3: Confidence Interval
o Now we want to see how well our data represents the entire population of Woodinville Bicycle customers. We will use the information from the sample to find the 95% confidence interval of the population mean.
§ First, we need to find the margin of error: (2 x σ )/
· (2 x 4.8635)/ = 0.9727. The margin of error is 0.9727.
§ We get the 95% confidence interval by subtracting and adding the margin of error from/to the sample set’s mean: 9.27-0.9727=8.2973 and 9.27+0.9727=10.2427
§ The data supports with 95% confidence that the population mean falls between 8.2973 and 10.2427 (8.2973<μ<10.2427).
Graphical Representation: Frequency Chart
Discussion:
I found the information gathered from the data very interesting; the mean, median, and mode were all between 9 and 10 hours per week, a third of WB cyclists ride between about 7 and 12 hours per week, and the confidence interval puts the population mean between just above 8 to just above 10 hours per week. The chart shows that the most frequent answers given were between 8 and 12 hours. This is interesting to me because all of the analyses of data line up quite nicely, and give us a very clear picture of the riding habits of Woodinville Bicycle customers.
There are a few uncertainties in the data collected, however, and I feel that a more thorough sampling method may provide different results. First, the only people involved in taking the survey were customers who I helped on the days that I work (which is Thursday through Sunday.) Second, cyclists may have accidentally over or under estimated the amount of time they spend riding, or they could have given a false number. Given these possible sampling errors, I think the data gave good insight and a good estimate of the number of hours per week all Woodinville Bicycle customers ride per week.
Posted June 6, 2013 9:22 PM Pacific Time
