Introduction to Business Statistics I Homework # 2
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- Collin Briggs
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1 Introduction to Business Statistics I Homework # 2 Problem # 1 Consider this set of data a. Construct a frequency, relative frequency, and percentage distributions. - Let us take 5 classes with the lower limit of the first class equals 1.0. Class Tally Frequency Relative Freq. Percentage 1.0 to less than /39 = % 2.0 to less than /39 = % 3.0 to less than /39 = % 4.0 to less than /39 = % 5.0 to less than /39 = % sum = % b. Construct a relative frequency histogram. c. Describe the shape of data distribution. - Symmetric. d. Construct a cumulative distribution. Class Cumulative frequency 1.0 to less than to less than to less than to less than to less than
2 e. Draw an Ogive plot. f. What fraction of the measurements are 3.9 or less? - 17/39 = g. What fraction of the measurements are larger than 3.9? - 12/39 = h. Construct a stem and leaf plot. Stem units: 1 s, leaf units = i. Use the stem and leaf plot to find the smallest observation j. Compare the relative frequency histogram with the stem and leaf plot. Are the shapes similar? - Yes, almost the same.
3 Problem # 2 A discrete variable can take on only the values 0, 1, 2, or 3. A set of 30 measurements on this variable is shown here: a. Construct a relative frequency histogram. b. Create a dot plot. Bin Frequency Relative Frequency Total c. What proportion of the measurements are greater than 1? d. What proportion of the measurements are less than or equal to 2? e. Create a bar graph.
4 Problem # 3 Twenty elementary school children were asked if they live with parents (B), father only (F), mother only (M), or someone else (S). The responses of the children are as follow M B B M F S B M F B B F B M M B B F B M a. Construct a frequency distribution table. Category Tally Frequency B 9 F 4 M 6 S 1 sum =20 b. Write the relative frequencies and percentages for all categories. Category Relative Freq. Percentage B 9/20 = % F 4/20 = % M 6/20 = % S 1/20 = % % c. What percentage of the children in this sample live with mother only? - From the percentage column, the answer is 30.0%
5 Problem # 4 The following table lists the sales of four as shown on TV salespeople to costumers in three countries on certain days. Sale Country Salesperson Date of sale Sale Country Salesperson Date of sale Sale Country Salesperson Date of sale 1 Bahrain Nasser 20/7/ Qatar Salem 22/7/ Kuwait Ahmad 22/7/ Bahrain Nasser 20/7/ Bahrain Mohammad 22/7/ Kuwait Ahmad 22/7/ Qatar Mohammad 20/7/ Kuwait Ahmad 22/7/ Qatar Salem 23/7/ Bahrain Nasser 20/7/ Kuwait Ahmad 22/7/ Kuwait Ahmad 23/7/ Bahrain Nasser 20/7/ Bahrain Mohammad 22/7/ Kuwait Mohammad 23/7/ Qatar Mohammad 20/7/ Qatar Mohammad 22/7/ Qatar Salem 23/7/ Kuwait Nasser 21/7/ Qatar Nasser 22/7/ Kuwait Ahmad 23/7/ Qatar Mohammad 21/7/ Kuwait Ahmad 22/7/ Kuwait Nasser 23/7/ Bahrain Mohammad 21/7/ Qatar Salem 22/7/ Qatar Salem 23/7/ Kuwait Salem 21/7/ Bahrain Mohammad 22/7/ Kuwait Ahmad 23/7/ Kuwait Nasser 21/7/ Kuwait Ahmad 22/7/ Kuwait Mohammad 23/7/ Qatar Mohammad 21/7/ Kuwait Ahmad 22/7/ Qatar Salem 23/7/ Bahrain Mohammad 21/7/ Bahrain Mohammad 22/7/ Kuwait Ahmad 23/7/ Kuwait Salem 21/7/ Kuwait Salem 22/7/ Kuwait Mohammad 24/7/ Bahrain Mohammad 22/7/ Bahrain Mohammad 22/7/ Kuwait Ahmad 24/7/ Kuwait Salem 22/7/ Qatar Mohammad 22/7/ Kuwait Nasser 24/7/ Bahrain Mohammad 22/7/ Qatar Nasser 22/7/ Kuwait Mohammad 24/7/ Qatar Mohammad 22/7/ Kuwait Ahmad 22/7/ Bahrain Salem 24/7/ Qatar Nasser 22/7/ Qatar Salem 22/7/ Bahrain Ahmad 24/7/ Kuwait Ahmad 22/7/ Bahrain Mohammad 22/7/ Qatar Mohammad 24/7/2007 a. Construct a cross-tabulation between i. Salesperson and Date of Sale Date of sale Salesperson 20/7/ /7/ /7/ /7/ /7/2007 Grand Total Ahmad Mohammad Nasser Salem Grand Total ii. Salesperson and Country Country Salesperson Bahrain Kuwait Qatar Grand Total Ahmad Mohammad Nasser Salem Grand Total
6 b. Calculate the percentage of sales of the four salespersons out of the 60 items sold in the four day period. Salesperson frequency relative frequency percentage Ahmad Mohammad Nasser Salem Total
7 Problem # 5 Consider this stem and leaf plot: Stems unit: 10 s, leaf unit: 1 s Write the data set that was used to construct the display
8 Problem # 6 The following 25 observations are for two quantitative variables, x and y. x y x y x y x y x y a. Construct a scatter diagram for the relationship between x and y. b. What is the relationship, if any, between x and y. - From the scatter plot, one can see that there is positive (direct) linear relationship between x and y.
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