Data Analysis, Statistics, and Probability Practice Problems: GED Math

Answers

1. b.   To find the mean of a set of data, add up all the numbers and divide by the amount of data. 96 + 90 + 78 + 90 + 92 = 446. There are five data items. 446 ÷ 5 = 89.2, choice b.
2. c.   To find the mean fuel efficiency, add up the six numbers and divide by 6: 16 + 22 + 14 + 28 + 16 + 12 = 108, and 108 ÷ 6 = 18 miles per gallon.
3. c.   To answer this question, calculate the mean, median, and mode of the set of numbers. First, arrange the numbers in ascending order: 26, 27, 27, 27, 29, 29, 30, 30. There are eight numbers; add them together and divide by 8 for the mean: 26 + 27 + 27 + 27 + 29 + 29 + 30 + 30 = 225, and 225 divided by 8 is 28.125, which is the mean. The mode is the number that occurs most often, which is 27. The median is the middle number; since there are eight entries, it is the average of the two middle numbers: 27 + 29 = 56, and 56 divided by 2 is 28. Knowing the three measures can lead to the only right conclusion, which is that the median is greater than the mode, choice c.
4. b.   There is no number value repeated, so there is no mode.
5. a.   Probability is a ratio of number of favorable outcomes/number of total outcomes. There are six sides to a die, so there are six total outcomes, one of which is a 3. The probability is therefore .
6. b.   The steepest rise on the graph was from April 23 to April 30. The symbol indicates that it was in the Midwest.
7. d.   The prices for the West Coast have been rising steadily by 2 or 3 cents each week. On May 7, the price on the West Coast is a little beneath $2.80. If it rises 2 or 3 cents, it should be at about $2.82 by the following week. The question gives no reason to expect a sudden decline in price or a sharp increase.
8. e.   Look for the first year in which the bar that represents the number of women receiving bachelor's degrees is taller than the bar that represents the number of men receiving bachelor's degrees.

The first time this occurs is for 1989–1990.

9. c.   To solve the problem, first find how many women and how many men received bachelor's degrees in 1989–1990. For women, the height of the bar is a little past the middle between 500,000 and 600,000, at approximately 560,000. For men, the bar is at approximately 500,000. Subtract the estimates: 560,000 – 500,000 = 60,000.

Approximately 60,000 more women received bachelor degrees in 1989–1990.

10. b.   To find the mean, add up all of the data values, and divide by the number of items, which is eight: 32 + 34 + 34 + 35 + 37 + 38 + 34 + 42 = 286; 286 divided by 8 is 35.75.
11. e.   There are two modes for this data set. Both 71 and 68 appear in the set twice.
12. a.   First, arrange the data into increasing order: 8, 9, 9, 9, 10, 10, 11, 12, 13, 17. There is an even number of data values, so the median is the mean of the two middle values. They are both 10, so the median is 10. The middle values are 10 + 10 = 20, and 20 divided by 2 is 10.
13. b.   The range is the difference between the highest and lowest values in the set of data. The highest temperature is 84° and the lowest temperature is 42°: 84° – 42° = 42°.
14. e.   Use a table to find all of the possible sum outcomes when rolling two dice. From a table, you will see that there are 36 total outcomes, five of which generate a sum of 8. The sums of 8 are circled on the chart: 6 and 2, 2 and 6, 3 and 5, 5 and 3, and 4 and 4. The probability is therefore: number of favorable outcomes/number of total outcomes =
15. a.   Subtract hourly earnings of previous year from given year.
    1. 1992–1991 = $10.57 – $10.32 = $0.25
    2. 1994–1993 = $11.12 – $10.83 = $0.29
    3. 1996–1995 = $11.82 – $11.43 = $0.39
    4. 1997–1996 = $12.28 – $11.82 = $0.46
    5. 1998–1997 = $12.77 – $12.28 = $0.49

Compare differences to find the least difference. $0.25 is the least difference, which means 1992 had the least increase in hourly earnings from the previous year.

16. c.   Subtract to find the amount of increase.

1996 hourly earnings – 1990 hourly earnings

$11.82 – $10.01 = $1.81

Write a ratio comparing the amount of increase to the original amount: .

Change to a percent by first expressing the faction as decimal and then changing the decimal to a percent.

1.81 ÷ 10.01 ≈ = 0.1808

0.1808 = 18.08% ≈ 18%

17. c.   Use the table to find the total number of cars sold in the United States in 1998. total sales in 1998 = 8,141,721

Use the bar graph to find what percent of total car sales in 1998 small cars represented. small car sales in 1998 = 24.7%

Estimate 24.7% of 8,141,721 to find the approximate number of cars sold.

24.7% ≈ 25% =

8,141,721 ≈ 8,000,000

× 8,000,000 = 2,000,000

Approximately 2,000,000 small cars were sold in 1998.

18. d.   Use the graph to find the percent of sales for midsize, luxury, and large cars.

midsize: 52.7%

luxury: 16.5%

large: 7.6%

Find the sum of the percentages of luxury and large car sales.

16.5 + 7.6 = 24.1

Find the ratio of midsize car sales to the sum of luxury and large car sales.

52.7:24.1

This is about 2 to 1. About twice as many midsize cars as luxury and large cars combined were sold in 1998.