3. Given the following measures of center for a data set, describe the most like

Question

3. Given the following measures of center for a data set, describe the most likely shape of the distribution (symmetric, skewed left, skewed right). Briefly explain your reasoning a. Mean= 122, Median= 164, Mode= 165 b, Mean= 164, Median= 164, Mode=164 Mean= 165, Median= 164, Mode= 122 4. In a study investigation car speed in automobile accidents, 5000 accidents were examined and the vehicle speed at impact was recorded. Suppose the average speed at impact in the study was 42 mph with a standard deviation of 15 mph. A histogram of the data revealed that the distribution of speeds was approximately normal (symmetric bell curve) a. Approximately what percent of the vehicle speeds were between 12 mph and 57 mph? b. Approximately what percent of the vehicle speeds were less than 12 mph? C. Approximately what percent of the vehicle speeds were less than 57 mph? 5. The following stem-and-leaf plot lists the average mpg for 30 different makes of car What is mpg of the car in the 10th percentile? What is the mpg of the car in the 65th percentile? The Nissan Murano has an average mpg of 23. In what percentile is this value? The Kia Forte has an average mpg of 31. In what percentile is this value? a. b. C. d.

Explanation / Answer

3.

a.

When mean is left of median is left of mode i.e. Mode>Median>Mean then distribution is left skewed

165 >164>122 It is left skewed
Please note that median is almost equal to mode

b.
Mean is equal to median and mode . So, it is a symmetrical distribution
The mean is not skewed by outliers in this case, i.e. the 3 stats are aligned

c. Is is right skewed. Why? The outliers at right, shift the mean right, though the concentration of point is more towards left( i.e. median and mode are to the left.

2.

We have been given the params of normal distribution ( safe to assume normality as n>>30 at 5000)

Mean = 42, stdev = 15. We will use these params to convert the X variable to Z.

a.P(12<X<57) = P(12-42/15<Z<57-42/15) = P(-1.8<Z<1) = .8413-.0359 = .8054
b.P(X<12) = P(Z< 12-42/15) = P(Z<-1.8) = .0359
c.P(X<57) = P(Z<57-42/15) = P(Z<1) = .8413

3. Pls post the stem leaf plot, it' not there in the question

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