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Statistical Analysis and Data Interpretation: Practical Applications and Problem Solving - Document preview page 1

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Statistical Analysis and Data Interpretation: Practical Applications and Problem Solving

This solved assignment covers statistical analysis methods and data interpretation, including real-world problem-solving applications.

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Statistical Analysis and Data Interpretation: Practical Applications and Problem Solving - Page 1 preview imageStatistical Analysis and Data Interpretation: Practical Applications andProblem SolvingQuestion 1:At the PISA Web site (www.pisa.oecd.org), there are summary statistics formath scores of 15-year-old males and females for various countriesseparately. The meanmath scores for males, themean math scores for females, and also the difference of the twomeans are listed in the Excelfile.a. Use any software and obtain the histogram for the mean math scores for males.b. How would you describe the overall shape of this data set? Do you suspect any outlyinggroupin this data set?The shape of distribution of the mean math scores for males is approximately normal.Thevalues 400 and 420seemto be outliers in this data set.c. Reportthe 5-number summaries for the difference of the two means. (Note: Don’t usesoftware. Use the method discussed in class).The ordered series of the differences is shown in the table below.-555667789999101010
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Statistical Analysis and Data Interpretation: Practical Applications and Problem Solving - Page 3 preview image101111131314141415161717192023Minimum =5(N+1)/4 = 31/4 = 7.75First Quartile = 7thterm + .75 (8thterm7thterm) = 7 + .75 (87) = 7.75Median = Mean of two middle terms, i.e. 15thand 16thterms = (10 + 10)/2 = 103(N+1)/4 =3(31)/4 =23.25ThirdQuartile =23rdterm+ .25 (24thterm23rdterm) =14 + .25 (1514) =14.25Maximum = 23d. Obtain the back-to-back stemplot and compare the distribution of the mean mathscores formales and for females.FemaleMale140410142743443 7 9454620 6470 4 92 5 6 7 74841 2 4 4 6493 6 8 9 90 4 8 8500 3 4 5 73 3 7 7513 4 7 80 3 4524 7 7533 4 6 73 354552 4Back to Back Stem-and-Leaf PlotStem unit: 10
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Statistical Analysis and Data Interpretation: Practical Applications and Problem Solving - Page 4 preview imagee. Use any software andreport the sample mean and sample standard deviation for themeanmath scores for females.The sample mean forthemean math scores for females= 492.13The sample standard deviation forthemean math scores for females= 31.61f. Based on thegiven data, what proportion of the mean math scores for females fallswithin 2standard deviation of the mean?The required range for the mean math scores for females within 2 standard deviations ofthe mean is,[492.132 (31.61), 492.132 (31.61)] = [428.91, 555.35].Therefore, the number of mean math scores for females falls within the range [428.91,555.35] is28.The proportion of the mean math scores for females falls within 2 standard deviation of themean is,𝟐𝟖𝟑𝟎=𝟎.𝟗𝟑𝟑𝟑Question 3:Question 3: The amount of sodium is recorded for each of the 200 randomly selected9-ounceserving of chicken noodle soup which yields a mean of 1100 mg and a standarddeviation of 150mg. Moreover, the data distribution looks approximately bell-shaped.Descriptive statisticsFemalescount30mean492.13sample variance999.29sample standard deviation31.61
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