Quiz : How Much You Know About Measures Of Central Tendency?

1. Which of the following is NOT an example of a measure of central tendency?

Mean

Range

Median

Mode

The range is not an example of a measure of central tendency because it measures the dispersion or spread of data rather than its central value. Measures of central tendency, such as the mean, median, and mode, are used to describe the typical or central value of a dataset. The range, on the other hand, simply calculates the difference between the maximum and minimum values in the dataset, providing information about the variability or spread of the data points.

Explanation

The range is not an example of a measure of central tendency because it measures the dispersion or spread of data rather than its central value. Measures of central tendency, such as the mean, median, and mode, are used to describe the typical or central value of a dataset. The range, on the other hand, simply calculates the difference between the maximum and minimum values in the dataset, providing information about the variability or spread of the data points.

2. To calculate the median correctly, what must be done?

Arrange all the data in random order

Add all the data

Arrange all the data in an ascending or descending order

All of the above

To calculate the median correctly, it is necessary to arrange all the data in an ascending or descending order. This is because the median is the middle value of a dataset when it is ordered. By arranging the data in a specific order, it becomes easier to identify the middle value and accurately calculate the median. Arranging the data in random order or adding all the data would not provide the correct result for calculating the median.

Explanation

To calculate the median correctly, it is necessary to arrange all the data in an ascending or descending order. This is because the median is the middle value of a dataset when it is ordered. By arranging the data in a specific order, it becomes easier to identify the middle value and accurately calculate the median. Arranging the data in random order or adding all the data would not provide the correct result for calculating the median.

3. Find the mean of the data below. 7, 23, 11, 32, 9

11

16.4

25

7

The mean is calculated by adding up all the numbers in the data set and then dividing by the total number of values. In this case, the sum of the numbers is 7 + 23 + 11 + 32 + 9 = 82. Since there are 5 numbers in the data set, the mean is 82 divided by 5, which equals 16.4.

Explanation

The mean is calculated by adding up all the numbers in the data set and then dividing by the total number of values. In this case, the sum of the numbers is 7 + 23 + 11 + 32 + 9 = 82. Since there are 5 numbers in the data set, the mean is 82 divided by 5, which equals 16.4.

4. If a data set has an outlier, which measure of central tendency would be the best measure of the middle to use?

Mean

Median

Mode

Range

When a data set has an outlier, the best measure of central tendency to use is the median. The median is the middle value of a data set when it is arranged in ascending or descending order. Unlike the mean, which is greatly influenced by outliers, the median is not affected by extreme values. Therefore, it provides a more accurate representation of the middle value in a data set that contains outliers. The mode is not applicable in this case since it represents the most frequently occurring value, and the range only provides information about the spread of the data.

Explanation

When a data set has an outlier, the best measure of central tendency to use is the median. The median is the middle value of a data set when it is arranged in ascending or descending order. Unlike the mean, which is greatly influenced by outliers, the median is not affected by extreme values. Therefore, it provides a more accurate representation of the middle value in a data set that contains outliers. The mode is not applicable in this case since it represents the most frequently occurring value, and the range only provides information about the spread of the data.

5. What does percentile do?

Divides the set into two equal parts

Add all the given sets

Divides the set into 100 equal parts

Option 4

Percentile is a statistical measure that divides a set of data into 100 equal parts. It represents the percentage of values below a certain point in the data set. For example, if a student scores in the 80th percentile on a test, it means that their score is higher than 80% of the other scores. Therefore, the correct answer is "Divides the set into 100 equal parts."

Explanation

Percentile is a statistical measure that divides a set of data into 100 equal parts. It represents the percentage of values below a certain point in the data set. For example, if a student scores in the 80th percentile on a test, it means that their score is higher than 80% of the other scores. Therefore, the correct answer is "Divides the set into 100 equal parts."

6. Your county is conducting a survey to determine the mean annual income per household. Which of the following sampling methods would be more likely to result in a representative sample?

A phone survey of 100 people between 2 and 3 pm.

Survey's sent to 100 single family homes.

Survey's sent to 100 homes that were randomly selected from a database of all county adults.

None of these

A survey sent to 100 homes that were randomly selected from a database of all county adults would be more likely to result in a representative sample because it ensures that every adult in the county has an equal chance of being selected. This method helps to minimize bias and increase the likelihood that the sample accurately represents the entire population. The other options, such as a phone survey during a specific time frame or surveys sent to single-family homes, may introduce selection bias and may not accurately reflect the entire population.

Explanation

A survey sent to 100 homes that were randomly selected from a database of all county adults would be more likely to result in a representative sample because it ensures that every adult in the county has an equal chance of being selected. This method helps to minimize bias and increase the likelihood that the sample accurately represents the entire population. The other options, such as a phone survey during a specific time frame or surveys sent to single-family homes, may introduce selection bias and may not accurately reflect the entire population.

7. Which of the following statements is NOT true about the two data sets below? Set A: 156, 175, 122, 141, 178, 111 147.17 148.5 Set B: 189, 210, 167, 100, 125, 143 155.67 155

The mean for Set A is approximately 9 more than Set B.

The man for Set A is approximately 9 less than Set B.

The median for Set A is 148.5.

The median for Set B is approximately 6 more than Set A.

The mean for Set A is not approximately 9 more than Set B because the mean for Set A is 147.17 and the mean for Set B is 155.67. The difference between the two means is approximately 8.5, not 9.

Explanation

The mean for Set A is not approximately 9 more than Set B because the mean for Set A is 147.17 and the mean for Set B is 155.67. The difference between the two means is approximately 8.5, not 9.

8. Which data set has a larger spread in the top 25%? Joy: 52, 67, 73, 81, 83, 89, 93 Chrystal: 68, 72, 73, 79, 84, 85 Jacob: 72, 75, 78, 81, 85, 89, 98 Sasha: 88, 89, 92, 95, 95, 96, 100

Joy

Chrystal

Jacob

Sasha

To find out which data set has the largest spread in the top 25%, we look at the highest 25% of each set and find the difference between the highest and lowest values.

Joy:

Data: 52, 67, 73, 81, 83, 89, 93

Top 25%: 89, 93

Spread: 93 - 89 = 4

Chrystal:

Data: 68, 72, 73, 79, 84, 85

Top 25%: 84, 85

Spread: 85 - 84 = 1

Jacob:

Data: 72, 75, 78, 81, 85, 89, 98

Top 25%: 89, 98

Spread: 98 - 89 = 9

Sasha:

Data: 88, 89, 92, 95, 95, 96, 100

Top 25%: 96, 100

Spread: 100 - 96 = 4

Jacob's data set has the largest spread in the top 25%, with a spread of 9.

Explanation

To find out which data set has the largest spread in the top 25%, we look at the highest 25% of each set and find the difference between the highest and lowest values.

Joy:

Data: 52, 67, 73, 81, 83, 89, 93

Top 25%: 89, 93

Spread: 93 - 89 = 4

Chrystal:

Data: 68, 72, 73, 79, 84, 85

Top 25%: 84, 85

Spread: 85 - 84 = 1

Jacob:

Data: 72, 75, 78, 81, 85, 89, 98

Top 25%: 89, 98

Spread: 98 - 89 = 9

Sasha:

Data: 88, 89, 92, 95, 95, 96, 100

Top 25%: 96, 100

Spread: 100 - 96 = 4

Jacob's data set has the largest spread in the top 25%, with a spread of 9.

9. Find the MAD for the data set below. 18, 15, 24, 12, 29, 31, 24, 19, 27

22.1

48.9

5.43

24

The mean absolute deviation (MAD) is a measure of the dispersion or spread of a data set. It is calculated by finding the absolute difference between each data point and the mean of the data set, and then taking the average of these differences. In this case, the given data set is 18, 15, 24, 12, 29, 31, 24, 19, 27. To find the MAD, we first calculate the mean of the data set, which is 22.1. Then, we find the absolute difference between each data point and the mean: |18-22.1|, |15-22.1|, |24-22.1|, |12-22.1|, |29-22.1|, |31-22.1|, |24-22.1|, |19-22.1|, |27-22.1|. Taking the average of these absolute differences, we get 5.43. Therefore, the MAD for this data set is 5.43.

Explanation

The mean absolute deviation (MAD) is a measure of the dispersion or spread of a data set. It is calculated by finding the absolute difference between each data point and the mean of the data set, and then taking the average of these differences. In this case, the given data set is 18, 15, 24, 12, 29, 31, 24, 19, 27. To find the MAD, we first calculate the mean of the data set, which is 22.1. Then, we find the absolute difference between each data point and the mean: |18-22.1|, |15-22.1|, |24-22.1|, |12-22.1|, |29-22.1|, |31-22.1|, |24-22.1|, |19-22.1|, |27-22.1|. Taking the average of these absolute differences, we get 5.43. Therefore, the MAD for this data set is 5.43.

10. How can you find the value of mode graphically?

Histogram

Pie chart

Bar graph

All of the above

A histogram is a graphical representation of data that uses bars to represent the frequency or count of different categories or intervals. The mode is the value or category that appears most frequently in the data. By examining the heights of the bars in a histogram, we can determine which category or interval has the highest frequency, thus identifying the mode graphically. Therefore, a histogram is a suitable tool for finding the value of mode graphically.

Explanation

A histogram is a graphical representation of data that uses bars to represent the frequency or count of different categories or intervals. The mode is the value or category that appears most frequently in the data. By examining the heights of the bars in a histogram, we can determine which category or interval has the highest frequency, thus identifying the mode graphically. Therefore, a histogram is a suitable tool for finding the value of mode graphically.