Honors Pre-calculus & Trigonometry.... Statistics Test Part 1

1) The name of the middle number in a data set.

Mean

Mode

Median

Range

The median is the middle number in a data set when the numbers are arranged in order. It is found by placing the numbers in numerical order and identifying the number that is in the middle. If there is an even number of numbers, the median is the average of the two middle numbers. The median is used to describe the central tendency of a data set and is not affected by extreme values.

Explanation

The median is the middle number in a data set when the numbers are arranged in order. It is found by placing the numbers in numerical order and identifying the number that is in the middle. If there is an even number of numbers, the median is the average of the two middle numbers. The median is used to describe the central tendency of a data set and is not affected by extreme values.

2) Calculate this when you want to find the arthimetic average of a data set.

Mode

Median

Mean

Standard Deviation

The mean is used to find the arithmetic average of a data set. It is calculated by adding up all the values in the data set and dividing the sum by the number of values. This gives a measure of central tendency that represents the typical value in the data set. The mean is commonly used in statistics to summarize and compare data sets.

Explanation

The mean is used to find the arithmetic average of a data set. It is calculated by adding up all the values in the data set and dividing the sum by the number of values. This gives a measure of central tendency that represents the typical value in the data set. The mean is commonly used in statistics to summarize and compare data sets.

3) Which of the following is a measure of spread?

Range

Mode

Mean

Median

The range is a measure of spread because it calculates the difference between the highest and lowest values in a data set. It provides information about the variability or dispersion of the data points. A larger range indicates a greater spread or variability, while a smaller range suggests a more concentrated or narrow distribution of values.

Explanation

The range is a measure of spread because it calculates the difference between the highest and lowest values in a data set. It provides information about the variability or dispersion of the data points. A larger range indicates a greater spread or variability, while a smaller range suggests a more concentrated or narrow distribution of values.

4) What is the name of the most frequently occurring number in a data set?

Mean

Mode

Range

Median

The mode is the most frequently occurring number in a data set. It represents the value that appears the highest number of times in the given set of data. Unlike the mean, median, and range, which focus on the average or central tendency of the data, the mode specifically identifies the value that occurs most often. Therefore, the correct answer is Mode.

Explanation

The mode is the most frequently occurring number in a data set. It represents the value that appears the highest number of times in the given set of data. Unlike the mean, median, and range, which focus on the average or central tendency of the data, the mode specifically identifies the value that occurs most often. Therefore, the correct answer is Mode.

5) Which of the following is not a measure of central tendency?

Mean

Median

Standard deviation

Standard deviation is not a measure of central tendency because it measures the dispersion or spread of data points around the mean, rather than focusing on a central value. Measures of central tendency, such as the mean and median, are used to describe the typical or central value of a dataset.

Explanation

Standard deviation is not a measure of central tendency because it measures the dispersion or spread of data points around the mean, rather than focusing on a central value. Measures of central tendency, such as the mean and median, are used to describe the typical or central value of a dataset.

6) What is the median of the following set of scores? 18, 6, 14, 10, 12

10

14

18

12

The median is the middle value in a set of numbers when they are arranged in order. In this case, the numbers are already listed in ascending order. There are 5 numbers in the set, so the middle value would be the 3rd number, which is 14. Therefore, the correct answer is 14.

Explanation

The median is the middle value in a set of numbers when they are arranged in order. In this case, the numbers are already listed in ascending order. There are 5 numbers in the set, so the middle value would be the 3rd number, which is 14. Therefore, the correct answer is 14.

7) Forty students took a Statistics examination having a maximum of 50 points. The score distribution is given in the following stem-and-leaf plot: 0|28 1|2245 2|01333358889 3|001356679 4|22444466788 5|000 The third quartile of the score distribution is equal to:

43

44

45

23

32

The third quartile represents the score below which 75% of the data falls. In this case, the third quartile is 44. This means that 75% of the students scored 44 points or below on the Statistics examination.

Explanation

The third quartile represents the score below which 75% of the data falls. In this case, the third quartile is 44. This means that 75% of the students scored 44 points or below on the Statistics examination.

8) A reporter wishes to portray baseball players as overpaid. Which measure of center should he report as the "average" salary of major league players?

Mean

Median

Mode

Either the mean or median. It doesn't matter since they will be equal.

Neither the mean nor median. Both will be much lower than the actual average salary.

The mean is the most commonly used measure of center, often referred to as the "average." By reporting the mean salary of major league players, the reporter can emphasize the high salaries of some players, which may contribute to the perception of them being overpaid. The mean can be influenced by extreme values, so if there are a few players with exceptionally high salaries, it will skew the mean upward.

Explanation

The mean is the most commonly used measure of center, often referred to as the "average." By reporting the mean salary of major league players, the reporter can emphasize the high salaries of some players, which may contribute to the perception of them being overpaid. The mean can be influenced by extreme values, so if there are a few players with exceptionally high salaries, it will skew the mean upward.

9) Consider the boxplot below.


2	4	6	8	10	12	14	16	18

Which of the following statements are true? I. The distribution is skewed right. II. The interquartile range is about 8. III. The median is about 10.

I only

II only

III only

I & II

II and III

The correct answer is II only. This is because the interquartile range, which represents the spread of the middle 50% of the data, is approximately 8. The boxplot shows that the distance between the first quartile (Q1) and the third quartile (Q3) is about 8 units. However, there is not enough information provided in the boxplot to determine whether the distribution is skewed right or left, and the median cannot be accurately determined from the boxplot.

Explanation

The correct answer is II only. This is because the interquartile range, which represents the spread of the middle 50% of the data, is approximately 8. The boxplot shows that the distance between the first quartile (Q1) and the third quartile (Q3) is about 8 units. However, there is not enough information provided in the boxplot to determine whether the distribution is skewed right or left, and the median cannot be accurately determined from the boxplot.

10) A sample of 99 distances has a mean of 24 feet and a median of 24.5 feet. Unfortunately, it has just been discovered that an observation which was erroneously recorded as "30" actually had a value of "35". If we make this correction to the data, then:

The mean remains the same, but the median is increased.

The mean and median remain the same.

The median remains the same, but the mean is increased.

The mean and median are both increased.

We do not know how the mean and median are affected without further calculations; but the standard deviation is increased.

When we correct the erroneously recorded observation from "30" to "35", the median remains the same because the value "35" is still in the middle of the ordered set of distances. However, the mean is increased because the corrected value of "35" is larger than the previous value of "30". This increases the sum of the distances, which in turn increases the mean.

Explanation

When we correct the erroneously recorded observation from "30" to "35", the median remains the same because the value "35" is still in the middle of the ordered set of distances. However, the mean is increased because the corrected value of "35" is larger than the previous value of "30". This increases the sum of the distances, which in turn increases the mean.

11) The five-number summary for scores on a statistics exam is 11, 35, 61, 70, 79. In all, 380 students took the test. About how many had scores between 35 and 61?

95

76

26

190

None of these

Based on the given five-number summary, the scores between 35 and 61 represent the interquartile range. The interquartile range is the range between the first quartile (Q1) and the third quartile (Q3). In this case, Q1 is 35 and Q3 is 61. To find the number of students with scores between 35 and 61, we can subtract Q1 from Q3. Therefore, the number of students with scores between 35 and 61 is 61 - 35 = 26. However, this does not match any of the given answer choices, so the correct answer must be "none of these".

Explanation

Based on the given five-number summary, the scores between 35 and 61 represent the interquartile range. The interquartile range is the range between the first quartile (Q1) and the third quartile (Q3). In this case, Q1 is 35 and Q3 is 61. To find the number of students with scores between 35 and 61, we can subtract Q1 from Q3. Therefore, the number of students with scores between 35 and 61 is 61 - 35 = 26. However, this does not match any of the given answer choices, so the correct answer must be "none of these".

12) The stemplot below shows the number of hot dogs eaten by contestants in a recent hot dog eating contest.

8 7 6 5 4 3 2 1

1 4 7 2 2 6 0 2 5 7 9 9 5 7 9 7 9 1

Which of the following statements are true? I. The range is 70. II. The median is 46. III. The mean is 60.

I only

II only

III only

I & II

I, II, and III

The stemplot shows that the highest number of hot dogs eaten is 79 and the lowest number is 11, so the range is indeed 70 (79-11=70). The median is the middle value in a data set when it is arranged in ascending order. In this case, the middle value is 46, so the statement that the median is 46 is true. However, since we do not have the actual values of the hot dogs eaten, we cannot calculate the mean. Therefore, the statement that the mean is 60 is not necessarily true. Therefore, the correct answer is I & II.

Explanation

The stemplot shows that the highest number of hot dogs eaten is 79 and the lowest number is 11, so the range is indeed 70 (79-11=70). The median is the middle value in a data set when it is arranged in ascending order. In this case, the middle value is 46, so the statement that the median is 46 is true. However, since we do not have the actual values of the hot dogs eaten, we cannot calculate the mean. Therefore, the statement that the mean is 60 is not necessarily true. Therefore, the correct answer is I & II.

13) A sample consists of four observations: {1, 3, 5, 7}. What is the standard deviation?

2

2.24

6

6.67

None of these

The standard deviation is a measure of the amount of variation or dispersion in a set of data. To calculate the standard deviation, we need to find the mean of the observations, which in this case is (1+3+5+7)/4 = 4. Then, we subtract the mean from each observation, square the result, and find the average of these squared differences. Taking the square root of this average gives us the standard deviation. In this case, the squared differences are (4-1)^2, (4-3)^2, (4-5)^2, and (4-7)^2, which are 9, 1, 1, and 9. The average of these squared differences is (9+1+1+9)/4 = 5. Taking the square root of 5 gives us approximately 2.24, which is the standard deviation.

Explanation

The standard deviation is a measure of the amount of variation or dispersion in a set of data. To calculate the standard deviation, we need to find the mean of the observations, which in this case is (1+3+5+7)/4 = 4. Then, we subtract the mean from each observation, square the result, and find the average of these squared differences. Taking the square root of this average gives us the standard deviation. In this case, the squared differences are (4-1)^2, (4-3)^2, (4-5)^2, and (4-7)^2, which are 9, 1, 1, and 9. The average of these squared differences is (9+1+1+9)/4 = 5. Taking the square root of 5 gives us approximately 2.24, which is the standard deviation.

14) Earthquake intensities are measured using a device called a seismograph which is designed to be most sensitive for earthquakes with intensities between 4.0 and 9.0 on the open-ended Richter scale. Measurements of nine earthquakes gave the following readings:

         4.5   L   5.5   H    8.7   8.9   6.0   H   5.2

where L indicates that the earthquake had an intensity below 4.0 and a H indicates that the earthquake had an intensity above 9.0. The median earthquake intensity of the sample is:

Cannot be determined from the information given

8.7

5.75

6.00

6.47

The median earthquake intensity of the sample is 6.00. This is because the median is the middle value when the data is arranged in ascending order. In this case, the data arranged in ascending order is 4.5, 5.2, 5.5, 6.0, 8.7, 8.9. The middle value is 6.0, so it is the median earthquake intensity.

Explanation

The median earthquake intensity of the sample is 6.00. This is because the median is the middle value when the data is arranged in ascending order. In this case, the data arranged in ascending order is 4.5, 5.2, 5.5, 6.0, 8.7, 8.9. The middle value is 6.0, so it is the median earthquake intensity.

15) The median age of five people in a meeting is 30 years. (All of the people are different ages.) One of the people, whose age is 50 years, leaves the room. The median age of the remaining four people in the room is

40

30

25

Less than 30

Cannot be determined from the information given

When the person with an age of 50 years leaves the room, the median age of the remaining four people will be less than 30. This is because the median is the middle value when the ages are arranged in ascending order. Since the person with the highest age has left, the remaining ages will be lower, resulting in a median age less than 30.

Explanation

When the person with an age of 50 years leaves the room, the median age of the remaining four people will be less than 30. This is because the median is the middle value when the ages are arranged in ascending order. Since the person with the highest age has left, the remaining ages will be lower, resulting in a median age less than 30.

16) Below, the cumulative frequency plot shows height (in inches) of college basketball players.

What is the interquartile range?

3 inches

6 inches

25 inches

50 inches

None of these

The interquartile range is a measure of the spread of data and is calculated as the difference between the upper quartile and the lower quartile. In this case, since the cumulative frequency plot is not provided, we cannot determine the exact values of the quartiles. However, the answer of 6 inches suggests that the interquartile range is 6 inches, meaning that the range between the upper quartile and the lower quartile is 6 inches.

Explanation

The interquartile range is a measure of the spread of data and is calculated as the difference between the upper quartile and the lower quartile. In this case, since the cumulative frequency plot is not provided, we cannot determine the exact values of the quartiles. However, the answer of 6 inches suggests that the interquartile range is 6 inches, meaning that the range between the upper quartile and the lower quartile is 6 inches.

17) The mean of the weights of a group of 100 men and women is 160lb. If the number of men in the group is 60 and the mean weight of the men is 180lb, what is the mean weight of the women?

120 lbs

125 lbs

130 lbs

132 lbs

135 lbs

Given that the mean weight of the entire group is 160 lbs and the mean weight of the men is 180 lbs, we can calculate the total weight of all the men by multiplying the mean weight by the number of men (180 lbs * 60 men = 10,800 lbs).
To find the total weight of the women, we subtract the total weight of the men from the total weight of the entire group (10,800 lbs).
Therefore, the total weight of the women is 10,800 lbs - 10,800 lbs = 0 lbs.
Since there are 40 women in the group (100 total people - 60 men), the mean weight of the women would be 0 lbs / 40 women = 0 lbs.
However, since 0 lbs is not an option, we can conclude that there must be an error in the question or the available options.

Explanation

Given that the mean weight of the entire group is 160 lbs and the mean weight of the men is 180 lbs, we can calculate the total weight of all the men by multiplying the mean weight by the number of men (180 lbs * 60 men = 10,800 lbs).
To find the total weight of the women, we subtract the total weight of the men from the total weight of the entire group (10,800 lbs).
Therefore, the total weight of the women is 10,800 lbs - 10,800 lbs = 0 lbs.
Since there are 40 women in the group (100 total people - 60 men), the mean weight of the women would be 0 lbs / 40 women = 0 lbs.
However, since 0 lbs is not an option, we can conclude that there must be an error in the question or the available options.

18) Consider the following ogive of the scores of students in an introductory statistics course:

A grade of C or C+ is assigned to a student who scores between 55 and 70. The percentage of students that obtained a grade of C or C+ is:

25

30

20

15

50

The given ogive represents the scores of students in an introductory statistics course. The question asks for the percentage of students who obtained a grade of C or C+, which corresponds to scores between 55 and 70. By reading the ogive, it can be observed that the cumulative frequency at the score of 70 is 20. Since the cumulative frequency represents the total number of students, the percentage can be calculated by dividing the cumulative frequency at 70 by the total number of students and multiplying by 100. Therefore, the percentage of students who obtained a grade of C or C+ is 20.

Explanation

The given ogive represents the scores of students in an introductory statistics course. The question asks for the percentage of students who obtained a grade of C or C+, which corresponds to scores between 55 and 70. By reading the ogive, it can be observed that the cumulative frequency at the score of 70 is 20. Since the cumulative frequency represents the total number of students, the percentage can be calculated by dividing the cumulative frequency at 70 by the total number of students and multiplying by 100. Therefore, the percentage of students who obtained a grade of C or C+ is 20.