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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 Question 1: At t he PISA Web site (www.pisa.oecd.org), there are summary statistics for math scores of 15 - year - old males and females for various countries separately. The mean math scores for males, the mean math scores for females, and also the difference of the two means are listed in the Excel file. 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 outlying group in this data set? The shape of distribution of the mean math scores for males is approximately normal. The values 400 and 420 seem to be outliers in this data set. c. Report the 5 - number summaries for the difference of the two means. (Note: Don’t use software. Use the method discussed in class). The ordered series of the differences is shown in the table below. - 5 5 5 6 6 7 7 8 9 9 9 9 10 10 10

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    10 11 11 13 13 14 14 14 15 16 17 17 19 20 23 Minimum = – 5 (N+1)/4 = 31/4 = 7.75 First Quartile = 7 th term + .75 (8 th term – 7 th term) = 7 + .75 (8 – 7) = 7.75 Median = Mean of two middle terms, i.e. 15 th and 16 th terms = (10 + 10)/2 = 10 3 (N+1)/4 = 3( 31 ) /4 = 23.25 Third Quartile = 23 rd term + .2 5 ( 24 th term – 23 rd term) = 14 + .25 (15 – 14 ) = 14.25 Maximum = 23 d. Obtain the back - to - back stem plot and compare the distribution of the mean math scores for males and for females. Female Male 1 40 41 0 1 42 7 43 44 3 7 9 45 46 2 0 6 47 0 4 9 2 5 6 7 7 48 4 1 2 4 4 6 49 3 6 8 9 9 0 4 8 8 50 0 3 4 5 7 3 3 7 7 51 3 4 7 8 0 3 4 52 4 7 7 53 3 4 6 7 3 3 54 55 2 4 Back to Back Stem-and-Leaf Plot Stem unit: 10

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    e. Use any software and report the sample mean and sample standard deviation for the mean math scores for females. The sample mean for the mean math scores for females = 492.13 The sample standard deviation for the mean math scores for females = 31.61 f. Based on the given data, what proportion of the mean math scores for females falls within 2 standard deviation of the mean? The required range for the mean math scores for females within 2 standard deviations of the mean is, [492.13 – 2 (31.61), 492.13 – 2 (31.61)] = [428.91, 555.35]. Therefore, the number of mean math scores for females falls within the range [428.91, 555.35] is 28. The proportion of the mean math scores for females falls within 2 standard deviation of the mean is, 𝟐𝟖 𝟑𝟎 = 𝟎 . 𝟗𝟑𝟑𝟑 Question 3: Question 3: The amount of sodium is recorded for each of the 200 randomly selected 9 - ounce serving of chicken noodle soup which yields a mean of 1100 mg and a standard deviation of 150 mg. Moreover, the data distribution looks approximately bell - shaped. Descriptive statistics Females count 30 mean 492.13 sample variance 999.29 sample standard deviation 31.61

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