Chances Are: The Only Statistic Book You'll Ever Need
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Chances Are is the first book to make statistics accessible to everyone, regardless of how much math you remember from school.
Distribution of Hourly Wages Paid to Employees at the Friendly Financial Corporation, December 19, 2038 Class Interval Frequency Cumulative Frequency $ 5.00-$5.99 6 6 6.00-6.99 9 15 7.00-7.99 5 20 8.00-8.99 10 30 9.00-9.99 8 38 10.00 and over 12 50 Cumulative frequencies tell us how many numbers are below a certain value. The cumulative value of 30 tells us that 30 employees earned less than $9. And a cumulative frequency of 15 tells us that 15 employees
for example, we’ll work with percentages, which we’ll need when we begin percentiles in the chapter after that. And when we finally get to the normal distribution and the bell curve in Chapter 8, we’ll be drawing upon our knowledge of percentiles. Learning statistics on your own can be an extremely difficult task. So please don’t move on to any new material until you fully understand the preceding material. By that I mean you’re getting a high percentage of the problems right. And speaking of
computations converting scores into percentiles and percentiles into scores, do we use class intervals of $999,999? That would make for some pretty unwieldy computations. So just round off the range of the class interval to $1,000,000. Is there a clear dividing line between when we need to use true limits and when we can just use our class intervals? Unfortunately, there isn’t any clear dividing line. We saw that it is absurd to use true limits when the class intervals are relatively large. We
you’ll have to set up your own problems. Let’s return to the question of how closely height and weight are correlated. Suppose we’ve made these six observations: (5′6″, 150 lbs.), (5′8″, 170 lbs.), (5′9″, 160 lbs.), (5′11″, 200), (6′0″, 240), and (6′2″, 220). Fill in these observations in the X and Y columns of Table 10.8. Be sure to convert your heights into inches. And does it matter whether you make height or weight X? It doesn’t matter. Height could be X and weight could be Y. Or vice
$66,000). Use this information to fill in Table 10.10. (You can get rid of sets of three zeroes following the thousands of dollars of income.) Then compute the correlation between IQ and annual income, and compare your work with mine. Table 10.10 x X2 y y2 XY Solution: Table 10.11 x x2 y y2 XY 93 8,649 14 196 1,302 98 9,604 17 289 1,666 100 10,000 23 529 2,300 102 10,404 20 400 2,040 109 11,881 25 625 2,725 119 14,161 80 6,400 9,520 128 16.384 66 4.356 8.448 749 81,083 245 12,795 28,001 X̄