 # Statistics and Probability Questions

## Question

1. One measure of the difficulty of a golf course is it's length total distance in yards from tee to the hole for all 18 holes here are the histogram and summary statistics for the lengths of 45 golf course
a. what is the range of theses data lengths?
b. Between what lengths do the central 50% of these courses lie?
c. what summary statistics would you use to describe this data?
d. Write a brief description of these data shape, center, and spread

2. The boxplots display case prices in dollars of varieties of grapes by three different vineyards
a. which vineyard produces the most expensive grape
b. which vineyard produces the cheapest grape
c. which vineyard are the grapes generally more expensive
d. determine which sentences describe which vineyards
I. this vineyard has a typical case price of about 96.00
II. this vineyard has the most variable case price
III. this vineyard has an outlier

Select one of the following for answer.
a. I describes B, II describes B, III describes C.
b. I describes B and C, II describes C, III describes A
c. I describes C, II describes A, III describes B
d. I describes B and C, II describes A, III describes A

3. The ogive shown below is the distribution of monthly returns for a group of aggressive or high growth mutual funds over a period of 25 yr form 1979 to 1999 recall that an ogive or cumulative relative frequency graph shows the percent of cases at or below a certain value. thus this graph always begins at 0% and ends at 100%
a. estimate the median the median is what % round to the nearest whole number as needed
b. estimate the quartiles the lower quartile is what % round to the nearest whole number estimate the quartiles the upper quartile is what % round to the nearest whole number
c. Estimate the range and the IQR the range is what % the IQR is what % round to the nearest whole number
d. create a boxplot of the data I will provide the data for this one

4. A survey was conducted on the efficiency of workers. A recent report included the graph on the right showing a rapid rise in productivity Describe what is wrong with the graph
a. there is no scale provided on the horizontal axis
b. the scales are inconsistent. the horizontal axis is missing both its label and scale
c.there is nothing wrong with the graph
d. the scales re inconsistent
e. the horizontal axis is not labeled
f. the horizontal axis is missing both its label and scale. both axes do not have any units provided.

## Solution Preview

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1)
A) The range for a given set of data is MAX-MIN=6743-5139=1604
B) The middle 50% would consist of a one standard deviation difference from the median in both directions. So our range would be [5914-399.37,5888.84+399.37]=[5514.63,6313.37]. If the range were larger, e.g. 90%, we would use two standard deviations.
C) C. Typically median and IQR (interquartile range) are good summary statistics. If you look at part E, you can use context to determine the correct response.
D) The distribution is skewed to the left and multimodal. The center of the data is 3914 yards and the distribution has a spread of 624.5 yards...
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