Question 2 [Total Marks: 11] TM supermarket wants to investigate the amount of money spent in RM) in their store by shoppers from two different age groups in a month. The shoppers were divided into two age groups under 35 and over 35. A random sample of 1000 shoppers were surveyed. A grouped frequency distribution on the amount of money spend by the two age groups was calculated and presented, as shown in Table 2.i. 0 Table 2.1: The group frequency distribution for the amount of money spent (in RM) by two age groups Cumulative Cumulative Lower Upper Limit Percentage Percentage Limit Frequency Frequency Frequency Frequency Percentage Percentage (under 35) (Over 35) (RM) (RM) Frequency Frequency (under 35) (Over 35) (under 35) (Over 35) 100 56 20 15.1% 3.2% 15.1% 3.2% 100 200 71 420 19.1% 66.8% 34.23% 69.95% 200 300 79 24 21.3% 3.8% 55.53% 73.77% 300 400 97 17 26.1% 2.7% 81.67% 76.47% 400 500 53 28 14.3% 4.5% 95.95% 80.92% 500 600 14 32 3.8% 5.1% 99.73% 86.01% 600 700 0 36 0.0% 5.7% 99.73% 91.73% 700 800 1 21 0.3% 3.3% 100.00% 95.07% 800 900 0 16 0.0% 2.5% 100.00% 97.62% 900 1000 0 6 0.0% 1.0% 100.00% 98.57% 1000 1100 0 4 0.0% 0.6% 100.00% 99.21% 1100 1200 0 4 0.0% 0.6% 100.00% 99.84% 1200 1300 0 1 0.0% 0.2% 100.00% 100.00% 371 629 100% 100% (a) Interpret the figure 26.1% (in bold and blue-coloured cell) and 76.47% (in bold and light orange coloured cell) in the fifth and eighth column, respectively, from Table 2.1. [1 mark] The amount spent (in RM) by the two age groups were gathered, and some summary statistics are presented in Table 22. Table 2.2 Amount spent (RM) Amount spent (RM) over under 35 age (n=371) 35 age (n=629) Mean 277.81 Total amount spent in RM) 900098,61 Median 276.65 Mode WNA 154.74 Variance INN.57 55867.69 Standard deviation Coefficient of Variation (as in (6) Fill in the missing values in Table 2.2. Give all answers to two decimal places. [3 marks] Mean amount spent by shoppers under 35 age: Total amount spent by shoppers over 35 age: Standard deviation of amount spent by shoppers under 35 age: Standard deviation amount spent by shoppers over 35 age: Coefficient of Variation in spending for shoppers under 35 age: Coefficient of Variation in spending for shoppers over 35 age: () Explain why the mode is not available for amount spent under 35 age group. [1 mark] (d) Using the standard deviation and the coefficient of variation, briefly explain amount spent (in RM) by the shoppers for the two different age groups. [3 marks] Question 2 [Total Marks: 11] TM supermarket wants to investigate the amount of money spent in RM) in their store by shoppers from two different age groups in a month. The shoppers were divided into two age groups under 35 and over 35. A random sample of 1000 shoppers were surveyed. A grouped frequency distribution on the amount of money spend by the two age groups was calculated and presented, as shown in Table 2.i. 0 Table 2.1: The group frequency distribution for the amount of money spent (in RM) by two age groups Cumulative Cumulative Lower Upper Limit Percentage Percentage Limit Frequency Frequency Frequency Frequency Percentage Percentage (under 35) (Over 35) (RM) (RM) Frequency Frequency (under 35) (Over 35) (under 35) (Over 35) 100 56 20 15.1% 3.2% 15.1% 3.2% 100 200 71 420 19.1% 66.8% 34.23% 69.95% 200 300 79 24 21.3% 3.8% 55.53% 73.77% 300 400 97 17 26.1% 2.7% 81.67% 76.47% 400 500 53 28 14.3% 4.5% 95.95% 80.92% 500 600 14 32 3.8% 5.1% 99.73% 86.01% 600 700 0 36 0.0% 5.7% 99.73% 91.73% 700 800 1 21 0.3% 3.3% 100.00% 95.07% 800 900 0 16 0.0% 2.5% 100.00% 97.62% 900 1000 0 6 0.0% 1.0% 100.00% 98.57% 1000 1100 0 4 0.0% 0.6% 100.00% 99.21% 1100 1200 0 4 0.0% 0.6% 100.00% 99.84% 1200 1300 0 1 0.0% 0.2% 100.00% 100.00% 371 629 100% 100% (a) Interpret the figure 26.1% (in bold and blue-coloured cell) and 76.47% (in bold and light orange coloured cell) in the fifth and eighth column, respectively, from Table 2.1. [1 mark] The amount spent (in RM) by the two age groups were gathered, and some summary statistics are presented in Table 22. Table 2.2 Amount spent (RM) Amount spent (RM) over under 35 age (n=371) 35 age (n=629) Mean 277.81 Total amount spent in RM) 900098,61 Median 276.65 Mode WNA 154.74 Variance INN.57 55867.69 Standard deviation Coefficient of Variation (as in (6) Fill in the missing values in Table 2.2. Give all answers to two decimal places. [3 marks] Mean amount spent by shoppers under 35 age: Total amount spent by shoppers over 35 age: Standard deviation of amount spent by shoppers under 35 age: Standard deviation amount spent by shoppers over 35 age: Coefficient of Variation in spending for shoppers under 35 age: Coefficient of Variation in spending for shoppers over 35 age: () Explain why the mode is not available for amount spent under 35 age group. [1 mark] (d) Using the standard deviation and the coefficient of variation, briefly explain amount spent (in RM) by the shoppers for the two different age groups. [3 marks]
