Data Analysis and Statistics

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SAT Math › Data Analysis and Statistics

Questions 1 - 10
1

A penny is altered so that the odds are 3 to 2 against it coming up tails when tossed; a nickel is altered so that the odds are 4 to 3 against it coming up tails when tossed. If both coins are tossed; what are the odds of both coins coming up heads?

23 to 12 against

23 to 12 in favor

29 to 6 in favor

29 to 6 against

Even

Explanation

3 to 2 odds in favor of heads is equal to a probability of , which is the probability that the penny will come up heads. Similarly, 4 to 3 odds in favor of heads is equal to a probability of , which is the probability that the nickel will come up heads.

Since the tosses of the two coins are independent, multiply the probabilities. The probability that there will be two heads is

This is to 12 against both coins coming up heads.

2

Determine the mean:

Explanation

The mean is the average of all numbers in the data set.

Add the numbers, and divide the total sum by four, since there are four numbers.

The answer is:

3

Find the mode of the data set.

Explanation

The mode of a data set is the data point(s) that appear the most often.

In the data set for this problem, both 4 and 5 appear twice, and no other number appears more than twice.

So for this data set there are two modes, 4 and 5.

4

Stem_and_leaf

Above is the stem-and-leaf display for a group of test scores. Order the mean, the median, and the mode of the scores from least to greatest.

Mean, median, mode

Mean, mode, median

Mode, median, mean

Median, mean, mode

Median, mode, mean

Explanation

The scores represented can be found from matching the tens digits in the "stem" to the units digits that form the "leaves" in their row. For example, the "leaves" in the "5" row are "2 2 4 4 7 7 8", so the scores will be 52, 52, 54, 54, 57, 57, and 58.

There are 53 scores represented, so to find the median, look for the middle score, in position

.

As can be seen in this diagram, the score - the median - is 74.

Stem_and_leaf_1

The most frequently occurring "leaf" is the "6" in the "7" row, so the mode is 76.

The mean is the sum of the scores divided by 53. If we add the scores, we get

, the mean is

In ascending order, the values are mean, median, mode.

5

Stem_and_leaf

Above is the stem-and-leaf display for a group of test scores. Order the mean, the median, and the mode of the scores from least to greatest.

Mean, median, mode

Mean, mode, median

Mode, median, mean

Median, mean, mode

Median, mode, mean

Explanation

The scores represented can be found from matching the tens digits in the "stem" to the units digits that form the "leaves" in their row. For example, the "leaves" in the "5" row are "2 2 4 4 7 7 8", so the scores will be 52, 52, 54, 54, 57, 57, and 58.

There are 53 scores represented, so to find the median, look for the middle score, in position

.

As can be seen in this diagram, the score - the median - is 74.

Stem_and_leaf_1

The most frequently occurring "leaf" is the "6" in the "7" row, so the mode is 76.

The mean is the sum of the scores divided by 53. If we add the scores, we get

, the mean is

In ascending order, the values are mean, median, mode.

6

Determine the mean:

Explanation

The mean is the average of all numbers in the data set.

Add the numbers, and divide the total sum by four, since there are four numbers.

The answer is:

7

Find the mode of the data set.

Explanation

The mode of a data set is the data point(s) that appear the most often.

In the data set for this problem, both 4 and 5 appear twice, and no other number appears more than twice.

So for this data set there are two modes, 4 and 5.

8

A penny is altered so that the odds are 3 to 2 against it coming up tails when tossed; a nickel is altered so that the odds are 4 to 3 against it coming up tails when tossed. If both coins are tossed; what are the odds of both coins coming up heads?

23 to 12 against

23 to 12 in favor

29 to 6 in favor

29 to 6 against

Even

Explanation

3 to 2 odds in favor of heads is equal to a probability of , which is the probability that the penny will come up heads. Similarly, 4 to 3 odds in favor of heads is equal to a probability of , which is the probability that the nickel will come up heads.

Since the tosses of the two coins are independent, multiply the probabilities. The probability that there will be two heads is

This is to 12 against both coins coming up heads.

9

Stem_and_leaf

Above is the stem-and-leaf display for a group of test scores. Which of the following scores would come closest to being at the 70th percentile?

Explanation

The stem-and-leaf display represents 53 scores. The score at the 70th percentile would be the score that is greater than 70% of the 53 scores, or

scores.

We count up 38 scores from the bottom:

Stem_and_leaf_2

The 38th-lowest score is 78, which is the correct choice.

10

Stem_and_leaf

Above is the stem-and-leaf display for a group of test scores. Which of the following scores would come closest to being at the 70th percentile?

Explanation

The stem-and-leaf display represents 53 scores. The score at the 70th percentile would be the score that is greater than 70% of the 53 scores, or

scores.

We count up 38 scores from the bottom:

Stem_and_leaf_2

The 38th-lowest score is 78, which is the correct choice.

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