1.
What is the average of the following set of numbers: 4, 8, 12, 16, 20
Correct Answer
B. 12
Explanation
The mean, or average, of a set of numbers is determined by adding all the numbers together and then dividing by the number of items in the dataset. In the case of the numbers 4, 8, 12, 16, and 20, the total sum is 60. When you divide this total by 5, the number of items, you obtain a mean of 12. This value serves as a central point, representing the average outcome of the dataset, which can be particularly useful in understanding overall trends and for comparing different sets of data.
2.
Find the middle value in this series: 3, 5, 7, 9, 11
Correct Answer
B. 7
Explanation
The median is the middle value in a series that has been arranged in order of magnitude. For the sequence 3, 5, 7, 9, 11, when placed in ascending order, the number 7 is exactly in the middle, with two numbers on either side. This statistic is especially important as it provides a measure of the central tendency that is not skewed by outliers, which can distort the mean.
3.
Which number appears most frequently in this list: 2, 3, 4, 2, 5, 2, 3
Correct Answer
A. 2
Explanation
The mode is the number that appears most frequently in a data set. In the list comprising numbers 2, 3, 4, 2, 5, 2, 3, the number 2 is observed three times, which is more frequent than any other number. Identifying the mode is beneficial as it shows the most common or prevalent value within the dataset, offering insights into what is typical or popular among the observed values.
4.
Calculate the range of these numbers: 15, 22, 29, 36, 43
Correct Answer
B. 28
Explanation
To calculate the range of a set of numbers, one must subtract the smallest value from the largest value. For the numbers 15, 22, 29, 36, 43, the smallest number is 15 and the largest is 43. The difference, which is 28, represents the range. This measure is critical for understanding how spread out the data is, indicating the variability or dispersion within the set.
5.
What is the median of these values: 12, 18, 25, 30, 36
Correct Answer
B. 25
Explanation
The median of an ordered list such as 12, 18, 25, 30, 36 is identified by finding the middle number, which is 25 in this case. It divides the dataset in such a way that half of the numbers are lower and half are higher than the median. This division is crucial for understanding the distribution of data, especially in skewed distributions where the mean might be misleading.
6.
Identify the mode in this set of numbers: 10, 20, 10, 30, 40, 10
Correct Answer
A. 10
Explanation
In the dataset 10, 20, 10, 30, 40, 10, the number 10 appears most frequently, three times, distinguishing it as the mode. This valueâ€™s repetition highlights it as a common or dominant characteristic within the set. Modes are particularly useful in distributions that show a high frequency of a particular value, indicating common traits or preferences.
7.
Determine the mean of these numbers: 5, 10, 15, 20, 25
Correct Answer
A. 15
Explanation
For the numbers 5, 10, 15, 20, 25, calculating the mean involves summing all the numbers to get 75 and then dividing by the number of entries, which is 5. This calculation results in a mean of 15. This average is a significant statistical measure because it reflects the central point around which the dataset clusters, indicating the typical value within a set.
8.
What is the range of the following numbers: 6, 12, 18, 24, 30
Correct Answer
A. 24
Explanation
The range for the set of numbers 6, 12, 18, 24, 30 is calculated by subtracting the smallest number (6) from the largest number (30), yielding a range of 24. This statistical measure provides insight into the total spread or difference between the highest and lowest values in the set, offering a sense of the variation present.
9.
Choose the correct median for this list: 45, 50, 55, 60, 65
Correct Answer
B. 55
Explanation
In the sequence 45, 50, 55, 60, 65, finding the median involves identifying the middle value, which is 55 when the numbers are arranged in increasing order. This value is pivotal as it splits the dataset into two equal parts, where half the values are below and half are above, serving as a robust indicator of central tendency.
10.
Find the mode of these values: 8, 16, 8, 24, 32, 16, 8
Correct Answer
A. 8
Explanation
The number 8 is the most frequently occurring value in the dataset 8, 16, 8, 24, 32, 16, 8, appearing three times, making it the mode. This repetition shows that 8 is a significant figure in the dataset, representing the most commonly occurring value, which can be key in understanding patterns or trends within the group.