Page 248 - Applied Statistics And Probability For Engineers

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6-6 TIME SEQUENCE PLOTS 209

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manufacturing process (units are ): 953, 950, 948, 955, 951, 6-50. Reconsider the spot weld shear strength data in
949, 957, 954, 955. Exercise 6-23. Construct a box plot of the strengths and write
(a) Calculate the sample mean, sample variance, and standard an interpretation of the plot. How does the box plot compare
deviation. in interpretive value to the original stem-and-leaf diagram in
(b) Find the median. How much could the largest temperature Exercise 6-23?
measurement increase without changing the median value? 6-51. Reconsider the female engineering student height
(c) Construct a box plot of the data. data in Exercise 6-22. Construct a box plot of the heights and
6-46. Exercise 6-12 presents drag coefficients for the write an interpretation of the plot. How does the box plot com-
NASA 0012 airfoil. You were asked to calculate the sample pare in interpretive value to the original stem-and-leaf dia-
mean, sample variance, and sample standard deviation of gram in Exercise 6-22?
those coefficients. 6-52. Reconsider the water quality data in Exercise 6-24.
(a) Find the upper and lower quartiles of the drag coefficients. Construct a box plot of the concentrations and write an interpre-
(b) Construct a box plot of the data. tation of the plot. How does the box plot compare in interpretive
(c) Set aside the largest observation (100) and rework parts a value to the original stem-and-leaf diagram in Exercise 6-24?
and b. Comment on your findings.
6-53. Reconsider the golf ball overall distance data in
6-47. The following data are the temperatures of effluent at Exercise 6-25. Construct a box plot of the yardage distance
discharge from a sewage treatment facility on consecutive and write an interpretation of the plot. How does the box plot
days: compare in interpretive value to the original stem-and-leaf di-
agram in Exercise 6-25?
43 47 51 48 52 50 46 49
6-54. Reconsider the wine rating data in Exercise 6-27.
45 52 46 51 44 49 46 51
Construct a box plot of the wine ratings and write an interpreta-
49 45 44 50 48 50 49 50
tion of the plot. How does the box plot compare in interpretive
(a) Calculate the sample mean and median. value to the original stem-and-leaf diagram in Exercise 6-27?
(b) Calculate the sample variance and sample standard 6-55. Use the data on heights of female and male engineer-
deviation. ing students from Exercises 6-22 and 6-29 to construct
(c) Construct a box plot of the data and comment on the in- comparative box plots. Write an interpretation of the informa-
formation in this display. tion that you see in these plots.
6-48. Reconsider the golf course yardage data in Exercise 6-3. 6-56. In Exercise 6-44, data was presented on the cold start
Construct a box plot of the yardages and write an interpreta- ignition time of a particular gasoline used in a test vehicle. A
tion of the plot. second formulation of the gasoline was tested in the same ve-
6-49. Reconsider the motor fuel octane rating data in hicle, with the following times (in seconds): 1.83, 1.99, 3.13,
Exercise 6-14. Construct a box plot of the yardages and write 3.29, 2.65, 2.87, 3.40, 2.46, 1.89, and 3.35. Use this new data
an interpretation of the plot. How does the box plot compare along with the cold start times reported in Exercise 6-44 to
in interpretive value to the original stem-and-leaf diagram in construct comparative box plots. Write an interpretation of the
Exercise 6-14? information that you see in these plots.

6-6 TIME SEQUENCE PLOTS

The graphical displays that we have considered thus far such as histograms, stem-and-leaf
plots, and box plots are very useful visual methods for showing the variability in data.
However, we noted in Section 1-2.2 that time is an important factor that contributes to vari-
ability in data, and those graphical methods do not take this into account. A time series or
time sequence is a data set in which the observations are recorded in the order in which they
occur. A time series plot is a graph in which the vertical axis denotes the observed value of
the variable (say x) and the horizontal axis denotes the time (which could be minutes, days,
years, etc.) When measurements are plotted as a time series, we often see trends, cycles, or
other broad features of the data that could not be seen otherwise.