Praxis Core Math Statistics Graphs and Data Quiz

1. A dataset contains the values 8, 12, 15, 20, and 25. What is the mean?

14

16

18

20

To find the mean, add all the values together: 8 + 12 + 15 + 20 + 25 = 80. Then, divide the total by the number of values (5): 80 ÷ 5 = 16. Thus, the mean of the dataset is 16.

Explanation

To find the mean, add all the values together: 8 + 12 + 15 + 20 + 25 = 80. Then, divide the total by the number of values (5): 80 ÷ 5 = 16. Thus, the mean of the dataset is 16.

2. In a bar graph showing student test scores, the median score is 78. What does this tell you?

Half the students scored above 78 and half below

Most students scored 78

The average score is 78

78 is the highest score

The median score represents the middle value in a sorted list of scores. Therefore, with a median of 78, it indicates that half of the students scored above this value while the other half scored below it, reflecting the distribution of test scores rather than the average or most common score.

Explanation

The median score represents the middle value in a sorted list of scores. Therefore, with a median of 78, it indicates that half of the students scored above this value while the other half scored below it, reflecting the distribution of test scores rather than the average or most common score.

3. A fair six-sided die is rolled once. What is the probability of rolling a 3 or 4?

1/6

1/3

1/2

2/3

When rolling a fair six-sided die, there are six possible outcomes (1 through 6). The favorable outcomes for rolling a 3 or 4 are two (3 and 4). The probability is calculated by dividing the number of favorable outcomes by the total outcomes: 2/6, which simplifies to 1/3.

Explanation

When rolling a fair six-sided die, there are six possible outcomes (1 through 6). The favorable outcomes for rolling a 3 or 4 are two (3 and 4). The probability is calculated by dividing the number of favorable outcomes by the total outcomes: 2/6, which simplifies to 1/3.

4. Which measure of central tendency is most affected by extreme outliers?

Mode

Median

Mean

Range

The mean is the average of all data points and is sensitive to extreme values. When outliers are present, they can significantly skew the mean, making it unrepresentative of the data set. In contrast, the median and mode are less affected by extreme values, providing a more stable measure of central tendency.

Explanation

The mean is the average of all data points and is sensitive to extreme values. When outliers are present, they can significantly skew the mean, making it unrepresentative of the data set. In contrast, the median and mode are less affected by extreme values, providing a more stable measure of central tendency.

5. A scatter plot shows a strong negative correlation between variables X and Y. What does this mean?

As X increases, Y tends to increase

As X increases, Y tends to decrease

There is no relationship between X and Y

X causes Y to change

A strong negative correlation indicates that as one variable (X) increases, the other variable (Y) tends to decrease. This inverse relationship suggests that higher values of X are associated with lower values of Y, highlighting a consistent pattern between the two variables in the scatter plot.

Explanation

A strong negative correlation indicates that as one variable (X) increases, the other variable (Y) tends to decrease. This inverse relationship suggests that higher values of X are associated with lower values of Y, highlighting a consistent pattern between the two variables in the scatter plot.

6. The standard deviation of a dataset is 5. What does this indicate?

The average value is 5

Data points vary about 5 units from the mean

The range is 5

The median is 5

A standard deviation of 5 indicates that the data points in the dataset typically deviate from the mean by about 5 units. This measure reflects the extent of variation or dispersion in the dataset, showing how spread out the values are around the average.

Explanation

A standard deviation of 5 indicates that the data points in the dataset typically deviate from the mean by about 5 units. This measure reflects the extent of variation or dispersion in the dataset, showing how spread out the values are around the average.

7. A histogram shows the distribution of heights in inches: 60-65 (8), 65-70 (15), 70-75 (12), 75-80 (5). How many people are 70 inches or taller?

12

17

27

32

To find the number of people 70 inches or taller, add the frequencies of the height ranges 70-75 and 75-80. The 70-75 range has 12 people, and the 75-80 range has 5 people. Thus, 12 + 5 equals 17 individuals who are 70 inches or taller.

Explanation

To find the number of people 70 inches or taller, add the frequencies of the height ranges 70-75 and 75-80. The 70-75 range has 12 people, and the 75-80 range has 5 people. Thus, 12 + 5 equals 17 individuals who are 70 inches or taller.

8. A bag contains 3 red balls and 2 blue balls. If you draw without replacement, what is the probability of drawing 2 red balls in a row?

3/10

6/25

3/5

9/25

To find the probability of drawing 2 red balls in a row without replacement, calculate the probability of drawing the first red ball (3/5) and then the second red ball (2/4). Multiply these probabilities: (3/5) * (2/4) = 6/20, which simplifies to 3/10. Thus, the probability is 3/10.

Explanation

To find the probability of drawing 2 red balls in a row without replacement, calculate the probability of drawing the first red ball (3/5) and then the second red ball (2/4). Multiply these probabilities: (3/5) * (2/4) = 6/20, which simplifies to 3/10. Thus, the probability is 3/10.

9. In a box plot, the box represents which portion of the data?

The lowest 25%

The middle 50%

The highest 25%

All data points

In a box plot, the box illustrates the interquartile range (IQR), which encompasses the middle 50% of the data. This range is defined by the first quartile (25th percentile) and the third quartile (75th percentile), effectively showing where the central half of the data lies and highlighting its variability.

Explanation

In a box plot, the box illustrates the interquartile range (IQR), which encompasses the middle 50% of the data. This range is defined by the first quartile (25th percentile) and the third quartile (75th percentile), effectively showing where the central half of the data lies and highlighting its variability.

10. A line graph displays temperature over 7 days. The temperatures are 68, 70, 72, 71, 69, 70, 73. What is the mode?

68

70

71

73

The mode is the value that appears most frequently in a data set. In this case, the temperature of 70 occurs twice, while all other temperatures occur only once. Therefore, 70 is the mode of the given temperatures over the 7 days.

Explanation

The mode is the value that appears most frequently in a data set. In this case, the temperature of 70 occurs twice, while all other temperatures occur only once. Therefore, 70 is the mode of the given temperatures over the 7 days.

11. Two events are independent if the occurrence of one event does not affect the ____ of the other.

Two events are considered independent when the outcome of one event does not influence the likelihood of the other event occurring. This means that knowing the result of one event provides no information about the probability of the other event happening, maintaining their separate probabilities.

Explanation

Two events are considered independent when the outcome of one event does not influence the likelihood of the other event occurring. This means that knowing the result of one event provides no information about the probability of the other event happening, maintaining their separate probabilities.

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12. A pie chart divides a whole into parts. If one slice represents 25% of the total, how many degrees does it occupy?

25°

45°

90°

180°

A pie chart represents a full circle of 360 degrees. To find the degrees occupied by a slice that represents 25% of the total, multiply 360 by 0.25. This calculation results in 90 degrees, indicating that the slice occupies a quarter of the pie chart.

Explanation

A pie chart represents a full circle of 360 degrees. To find the degrees occupied by a slice that represents 25% of the total, multiply 360 by 0.25. This calculation results in 90 degrees, indicating that the slice occupies a quarter of the pie chart.

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14. A dataset has a mean of 50 and a standard deviation of 10. Approximately what percentage of data falls within one standard deviation of the mean?

50%

68%

95%

99.7%

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Praxis Core Math Statistics Graphs and Data Quiz

1. A dataset contains the values 8, 12, 15, 20, and 25. What is the mean?

2.

What first name or nickname would you like us to use?

2. In a bar graph showing student test scores, the median score is 78. What does this tell you?

3. A fair six-sided die is rolled once. What is the probability of rolling a 3 or 4?

4. Which measure of central tendency is most affected by extreme outliers?

5. A scatter plot shows a strong negative correlation between variables X and Y. What does this mean?

6. The standard deviation of a dataset is 5. What does this indicate?

7. A histogram shows the distribution of heights in inches: 60-65 (8), 65-70 (15), 70-75 (12), 75-80 (5). How many people are 70 inches or taller?

8. A bag contains 3 red balls and 2 blue balls. If you draw without replacement, what is the probability of drawing 2 red balls in a row?

9. In a box plot, the box represents which portion of the data?

10. A line graph displays temperature over 7 days. The temperatures are 68, 70, 72, 71, 69, 70, 73. What is the mode?

11. Two events are independent if the occurrence of one event does not affect the ____ of the other.

12. A pie chart divides a whole into parts. If one slice represents 25% of the total, how many degrees does it occupy?

13. The interquartile range (IQR) is calculated by subtracting the ____ quartile from the third quartile.

14. A dataset has a mean of 50 and a standard deviation of 10. Approximately what percentage of data falls within one standard deviation of the mean?

15. In a survey, 60% of respondents prefer Product A and 40% prefer Product B. If 500 people were surveyed, how many preferred Product A?