1) Given this data (home runs per season for two baseball players):
Player A: 13, 27, 26, 44, 30, 40, 34, 45, 44, 24, 32, 44, 39, 29, 44, 38, 47, 34, 40, 20
Player B: 3, 49, 32, 33, 39, 22, 42, 9, 9, 39, 52, 34, 24, 58, 70, 65, 32
For each player, find the mean, median, mode, range, variance and standard deviation. Who had the highest average? Who was the most consistent? Explain your answers.
For each player, obtain the 5 number summary and construct a box plot.
Use your calculator for as much of this as you wish. However, for player B, in addition build a table of rows and columns to calculate the standard deviation showing all the details. Compare with calculator.
2) Given this data (daily high temperatures for one month):
74,78,78,79,79,80,80,81,82,82,82,83,83,83,83,84,84,84,84,85,85,85,85,86,86,87,88,88,89,92,94
Create a frequency distribution table (class limits, class boundaries, frequencies) and histogram using 7 classes. Calculate the percentile rank for a temperature of 85.
3) For the following table relating years of schooling (x) to life expectancy (y), find and interpret r and r2, create the regression equation and use it to predict life expectancy for both 15 and 22 years of schooling. Are each of these predictions interpolated or extrapolated? Why or why not?
| Country |
(x) |
(y) |
Country |
(x) |
(y) |
| Australia |
20 |
80.4 |
India |
10 |
62.9 |
| Bolivia |
14 |
63.9 |
Romania |
14 |
71.3 |
| Botswana |
12 |
46.6 |
Rwanda |
9 |
43.4 |
| China |
11 |
72 |
South Africa |
13 |
53.4 |
| Ethiopia |
6 |
50.7 |
Spain |
16 |
80 |
| Iraq |
10 |
57.1 |
Sweden |
16 |
80.1 |
| Mexico |
13 |
74.9 |
United States |
16 |
77.4 |
4) For a, b, c, write the formula (ex. 7P4), expand it showing the detail calculations, and then evaluate it.
a. The number of arrangements (permutations) for 5 items taken altogether.
b. The number of arrangements (permutations) for 5 items taken 3 at a time
c. The number of ways to select (combinations) 3 items out of 5.
d. Find the probability that one card selected from a full deck is a picture card (K, Q, or J ), or a spade.
Event A = the probability of selecting a picture cord
Event B = the probability of selecting a spade
P(A or B) = P(A) + P(B) - P(A and B)
= (/52) + (/52) - (/52) = (/52)