Chapter 3.1- Measures of Center
Listed below are the pulse rates (beats per minute) from samples of adult males and females. Find the mean, and median for each of the two samples and then compare the two sets of results. Does there appear to be a difference? Male: 75 66 61 79 91 74 55 83 55 59 56 97 58 61 80 Female: 72 63 87 92 75 92 91 88 94 77 66 95 67 78 85
-The mean for males is 70 beats per minute and the mean for females is 81.5 beats per minute -The median for males is 66 beats per minute and the median for females is 85 beats per minute -The pulse rates for females appear to be higher than the pulse rates for males
An experiment was conducted to determine whether a deficiency of carbon dioxide in the soil affects the phenotype of peas. Listed below are the phenotype codes where 1 = smooth yellow, 2 = smooth green, 3 = wrinkled yellow, and 4 = wrinkled green. Do the results make sense? Find the mean, median, mode, and midrange 4 3 2 4 2 2 3 1 4 3 3 2 3 3
Mean phenotype code: 2.8 Median phenotype code: 3 Mode phenotype code: 3 Midrange phenotype code: 2.5 Only the mode makes sense since the data is nominal
Listed below are the highest amounts of net worth (in millions of dollars) of all celebrities. What do the results tell us about the population of all celebrities? Based on the nature of the amounts, what can be inferred about their precision? Find the mean, median, mode, and midrange 255 195 190 175 165 165 160 160 160 160
Mean: $178.5 million Median: $165 million Mode: $160 million Midrange: $207.5 million Apart from the fact that all other celebrities have amounts of net worth lower than those given, nothing meaningful can be known about the population The values all end in 0 or 5, so they appear to be rounded estimates
Listed below are the measured radiation emissions (A, B, C, D, E, F, G, H, I, J, and K respectively. The media often presents reports about the dangers of cell phone radiation as a cause of cancer. Cell phone radiation must be 1.6 W/kg or less. Find the mean, median, midrange, and mode 0.67 1.53 0.86 0.23 0.69 0.44 1.47 1.45 1.05 0.28 1.16
Mean: 0.894 W/kg Median: 0.86 W/kg Midrange: 0.88 W/kg Mode: none The maximum data value is the most relevant statistic, because it is closest to the limit of 1.6 W/kg and that cell phone should be avoided
Listed below are the jersey numbers of 11 players randomly selected from the roster of a championship sports team. What do the results tell us? Find the mean, median, mode, and midrange for the data. 44 31 71 48 57 45 23 36 78 10 32
Mean: 43.2 Median: 44 Mode: none Midrange: 44 The jersey numbers are nominal data and they do not measure or count anything, so the resulting statistics are meaningless
A magazine published a list consisting of the state tax on each gallon of gas. If we add the 50 state tax amounts and then divide by 50, we get 27.3 cents. Is the value of 27.3 cents the mean amount of state sales tax paid by all US drivers? Why or why not?
No, the value of 27.3 cents is not the mean because the 50 amounts are all weighted equally in the calculation, but some states consume mire gas than others, so the mean amount of state sales tax should be calculated using a weighted mean