Car Thefts Last summer, an insurance company researcher conducted a survey on th
ID: 3274248 • Letter: C
Question
Car Thefts Last summer, an insurance company researcher conducted a survey on the number of car thefts in a large city for a period of 30 days. The stem and leaf display shows the numbers of car thefts for the 30 days. (5|0 means 50 thefts on one day.) a) In the context of the problem, write an interpretation of the next to the bottom row of the display. b) Find the mean and standard deviation of the distribution. c) Find the median and IQR of the distribution. d) Describe the distribution using the descriptors used in the text (indicate shape, center, spread, and any unusual features using appropriate vocabulary and appropriate statistics) e) Write a short paragraph explaining when would you use mean and standard deviation to report the center and spread of a distribution and when would you instead use median and interquartile range (IOR)? f) Suppose the first data value was 46 thefts instead of 50. How would this affect the median and IQR? How would this affect the mean and standard deviation? (be specific and write in complete sentences)Explanation / Answer
A)
From the Stem and Leaf diagram we observe that the number of car thefts per day is greater then or equal to 50.
b)
The mean and standard deviation of the distribution is computed by using the average and standard deviation formula in EXCEL we get mean is equal to 60.73 and standard deviation is equal to 7.86
c)
From the EXCEL descriptive function we get the median as 60.50 and inter quartile range is 10.75
d)
By using the Stem and leaf diagram we observe that the distribution rightly skewed therefore the distribution is positively skewed, therefore the mean is usually greater than the median
e) when their is large outliers it is useful to use mean. More time we prefer mean instead of median because the theoretically development and measure related to mean is quit straight forward than the median.
to check the variability or spread we use standard deviation
f) if the first value is 46 instead of 50,the median and inter quartile doesn't change but we observe that mean value is decreases as 60.60 and spread (standard deviation increases as 8.08
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.