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Assesses and reinforces the student's understanding and ability to find the mean, median and mode of discrete data.
Questions and Answers
1.
The mean of a population is also known as the
A.
Moderator
B.
Average
C.
Base
Correct Answer B. Average
Explanation The mean of a population refers to the average value of a set of data points. It is calculated by summing up all the values in the population and dividing it by the total number of data points. Therefore, "average" is the correct answer as it accurately describes the concept of the mean in statistics.
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2.
The mean can be calculated by
A.
Listing all terms in numeric order and finding the midpoint
B.
Finding the most common term
C.
Dividing the sum of all terms by the population size
D.
Using a calculator
Correct Answer C. Dividing the sum of all terms by the population size
Explanation The mean is a measure of central tendency that represents the average value of a set of numbers. To calculate the mean, you need to add up all the numbers in the set and then divide the sum by the total number of values in the set, which is known as the population size. This method ensures that each value contributes equally to the overall average.
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3.
The mode is the most common term. A population can have
A.
No mode
B.
One mode
C.
More than one mode
D.
All of the above
Correct Answer D. All of the above
Explanation The mode is the most common term in a population. It is possible for a population to have no mode, meaning that there is no term that appears more frequently than any other. It is also possible for a population to have one mode, where there is a single term that appears more frequently than any other. Additionally, a population can have more than one mode, where multiple terms appear with the same highest frequency. Therefore, all of the given options are correct.
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4.
To find the median value of a population, the terms must first be ordered numerically.
A.
True
B.
False
Correct Answer A. True
Explanation In order to find the median value of a population, the terms must first be ordered numerically. This is because the median is the middle value in a set of numbers when they are arranged in ascending or descending order. By ordering the terms numerically, we can easily identify the middle value and determine the median.
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5.
To find the median of a population with an even number of terms, you must
A.
Find the mean of the two central terms
B.
Choose one of the two central terms
C.
Use the difference between the two central terms
D.
Say that there is no median
Correct Answer A. Find the mean of the two central terms
Explanation To find the median of a population with an even number of terms, you must find the mean of the two central terms. This is because the median represents the middle value of a dataset, and when there is an even number of terms, there is no single middle value. Therefore, the average of the two central terms is used as the median to represent the center of the distribution.
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6.
A population's mean can also be calculated by multiplying each value by its decimal proportion of the population, and taking the sum of these products
A.
True
B.
False
Correct Answer A. True
Explanation The statement is true because calculating the mean by multiplying each value by its decimal proportion of the population and taking the sum of these products is a valid method. This method is known as the weighted mean and is commonly used when different values in the population have different weights or proportions. By multiplying each value by its decimal proportion, we are giving more weight to values that are more representative of the population, resulting in a more accurate measure of the population's mean.
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7.
What is the mean of the population
1, 1, 2, 3, 5, 5, 5, 6, 34
(rounded to 1 decimal place)
Correct Answer 6.9
Explanation The mean of a set of numbers is calculated by adding up all the numbers in the set and then dividing the sum by the total number of values. In this case, the sum of the numbers is 62, and there are 9 numbers in the set. Dividing 62 by 9 gives us an average of 6.9, rounded to 1 decimal place.
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8.
What is the mode of the population
1, 1, 2, 3, 5, 5, 5, 6, 34
Correct Answer 5
Explanation The mode of a set of numbers is the value that appears most frequently. In this case, the number 5 appears three times, which is more than any other number in the set. Therefore, the mode of the population is 5.
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9.
What is the median of the population
1, 1, 2, 3, 5, 5, 5, 6, 34
Correct Answer 5
Explanation The median is the middle value of a set of numbers when they are arranged in order. In this case, the numbers are already arranged in ascending order. There are 9 numbers in the population, so the middle value would be the 5th number, which is 5. Therefore, the median of the population is 5.
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10.
How many terms are greater than the mean of the population
1, 1, 2, 3, 5, 5, 5, 6, 34
Correct Answer 1
Explanation In the given population, there is only one term that is greater than the mean. The mean of the population can be calculated by summing all the terms and dividing by the total number of terms. In this case, the sum of the terms is 62 and there are 9 terms in total. Therefore, the mean is 62/9 = 6.89. Since there is only one term (34) that is greater than the mean, the answer is 1.
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11.
An outlier is a term that has a value that is significantly different from the majority of the population. Which measure is influenced by outliers?
A.
Mean
B.
Median
C.
Mode
Correct Answer A. Mean
Explanation The mean is influenced by outliers because it takes into account all the values in a dataset, including the outliers. Outliers can greatly affect the mean by pulling it towards their extreme values. The mean is calculated by summing all the values and then dividing by the total number of values, so if there are outliers with very high or very low values, the mean will be skewed towards those outliers.
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12.
This is the same population as in the earlier questions, but with the highest value changed
What is the mean of the population
1, 1, 2, 3, 5, 5, 5, 6, 12
(rounded to 1 decimal place)
Correct Answer 4.4
Explanation The mean of a population is calculated by adding up all the values in the population and then dividing by the total number of values. In this case, the sum of the values is 40 and there are 9 values in the population. Therefore, the mean is 40 divided by 9, which is equal to 4.4.
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13.
This is the same population as in the earlier questions, but with the highest value changed
What is the median of the population
1, 1, 2, 3, 5, 5, 5, 6, 12
Correct Answer 5
Explanation The median of a population is the middle value when the data is arranged in ascending or descending order. In this case, the population is already arranged in ascending order. The middle value is 5, which is the same as the previous questions. Therefore, the median of the population is 5.
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14.
This is the same population as in the earlier questions, but with the highest value changed
What is the mode of the population
1, 1, 2, 3, 5, 5, 5, 6, 12
Correct Answer 5
Explanation The mode of a set of numbers is the number(s) that appear most frequently. In this population, the number 5 appears three times, which is more than any other number. Therefore, the mode of the population is 5.
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15.
This is the same population as in the earlier questions, but with the highest value changed
1, 1, 2, 3, 5, 5, 5, 6, 12
What measures were affected by changing the outlier value?
A.
Mean
B.
Median
C.
Mode
Correct Answer A. Mean
Explanation By changing the highest value in the population, the mean is affected. The mean is calculated by adding up all the values in the population and dividing by the number of values. Since the highest value has changed, the sum of the values will be different, resulting in a different mean. The median and mode, on the other hand, are not affected by the outlier value. The median is the middle value when the population is arranged in ascending order, and the mode is the value that appears most frequently.
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16.
Which measures will always be a true value from the population?
A.
Mean
B.
Median
C.
Mode
Correct Answer(s) B. Median C. Mode
Explanation The median and mode are measures that can be considered true values from the population because they are not affected by extreme values or outliers. The median is the middle value of a dataset when arranged in ascending or descending order, and it represents the central tendency of the data. The mode is the most frequently occurring value in a dataset, and it provides insight into the most common value or category. Unlike the mean, which can be influenced by extreme values, the median and mode provide a more robust representation of the population.