Analyzing Data Sets and Lottery Prizes: Unveiling Central Tendency Measures and Comparison of Statistical Values

1. The measures of central tendency are the mean (average), median (middle value), and mode (most frequent value). a. For the first set (64, 69, 72, 54, 89, 92, 54, 32), first arrange them in order: 32, 54, 54, 64, 69, 72, 89, 92. The mean is the sum divided by the number of values, so it's (32+54+54+64+69+72+89+92)/8 = 63.25. The median is the average of two middle values, in this case, it's (64+69)/2 = 66.5. There is no mode in this data set because no value appears more than once. b. For the second set (4.2, 11.5, 6.8, 5.2, 5.4, 6.3, 12.1, 11.5, 11.9, 7.8, 13.1, 5.8, 6.2), first arrange them in order: 4.2, 5.2, 5.4, 5.8, 6.2, 6.3, 6.8, 7.8, 11.5, 11.5, 11.9, 12.1, 13.1. The mean is (4.2+5.2+5.4+5.8+6.2+6.3+6.8+7.8+11.5+11.5+11.9+12.1+13.1)/13 = 7.7 (round to the nearest tenth). The median is the middle value, which is 6.8. The mode is 11.5 as it appears twice. 2. a. For the lottery prizes, first consider the entire prize pool. The total prize pool is $2,000,000 + $2,450,000 + $2,500 = $4,452,500. The total number of prizes is 2+7+10 = 19 so the mean (average) is $4,452,500/19 = $234,342.11. The median (middle value) is the 10th prize highest value when the prizes are lined up in order, which is $350,000. The mode being the most frequent value, is $350,000 as it was the prize amount 7 times. b. The median is greater than the mean. c. The mode is greater than the mean.