Problems-Data-Quantiles_ANSWERS

Data:Asymmetry&Quantiles
1.Make a stem-and-leaf display of the following data.
4652464042464037464052
323732524032524052464652
2.Below are the values of20loans,in thousands of dollars.
59.259.561.665.566.672.974.877.379.283.7
85.685.886.687.087.190.293.398.6100.2100.7
(i)Calculate the median.
The median is about84.65
(ii)Calculate thefirst and third quartiles.
Thefirst and third quartiles are about71.3and87.9. (iii)Calculate the26th and83rd percentiles.
The26th and83rd percentiles are about75.4and92.6. (iv)Draw a box plot of the data.
Dr Toche —Selected Problems
3
3.Walter Gogel Company is an industrial supplier of fasteners,tools,and springs.The amounts
of its invoices vary widely,from less than $20.00
to more than $400.00.Below is a box plot of 80invoices sent during the month of January.Write a brief report summarizing the invoice amounts.Report the values of the first and third quartiles,the median,and whether there is any skewness.If there are any outliers,approximate the value of these invoices.
20406080
Walter Gogel Company is an industrial supplier of fasteners, tools, and springs.
amounts of its invoices vary widely, from less than $20.00 to more than $400.00. Du
he month of January the company sent out 80
invoices. Here is a box plot of thes voices. Write a brief report summarizing the invoice amounts. Be sure to include i mation on the values of the first and third quartiles, the median, and whether there i
skewness. If there are any outliers, approximate the value of these invoices.*
050100150200250
4.McGivern Jewelers reported the shape,size,price,and cut grade for33of its diamonds.
(Dataset from the publisher.)
(i)Draw a box plot of the variable‘price’and comment on the result.Are there any outliers?
What is the median price?What are the values of thefirst and the third quartiles?
(ii)Draw a box plot of the variable‘size’and comment on the result.Are there any outliers?
What is the median price?What are the values of thefirst and the third quartiles?
(iii)Draw a scatter diagram of‘price’(on the vertical axis)and‘size’(on the horizontal axis).
Are the variables correlated?Does any point seem to be different from the others?
(iv)Draw a contingency table for the variables‘shape’and‘cut grade’.What is the most common cut grade?What is the most common shape?What is the most common combination of cut grade and shape?
5.Refer to the North Valley real estate data recorded on houses sold during the last year.Prepare
a report on the selling prices of the houses based on the answers to the following questions.
(i)Compute the minimum,maximum,median,and thefirst and the third quartiles of price.
Create a box ment on the distribution of house prices.
The boxplot shows that the distribution is positively skewed with about7outliers
on the right(the‘positive’side).This is confirmed by thefinding that mean>
median.A comparison of Bowley and Fisher-Pearson coefficients of skewness
shows that the positive skew is caused mainly by the presence of outliers.
(ii)Inspect a scatter diagram with price on the vertical axis and the size of the house on the horizontal.Is there a relationship between these variables?
The scatter diagram shows that price and size are positively correlated.
(iii)For houses without a pool,draw a scatter diagram with price on the vertical axis and the size of the house on the horizontal.Do the same for houses with a pool.How do the relationships between price and size for houses without a pool and houses with a pool compare?
The scatter diagrams for houses with a pool and without a pool show that the
correlation between price and size is roughly the same for houses with or without
a pool.The data for houses without a pool has one clear outlier,which does not
however affect the relationship much.The data for houses with a pool has more
observations at the high size-price end.However,plotting a regression line on top
of the scatter reveals that the size-price relation is stronger for houses with a pool.
Running a robust regression—instead of ordinary least squares—or running
a trimmed ols(outliers removed)—reveals that,for houses without a pool,the
positive association is weaker without the outlier.。