Mean, Median, Mode, And Range Quiz

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.

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.

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.

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.

In the dataset 10, 20, 10, 30, 40, 10, the number 10 appears most frequently, three times, distinguishing it as the mode. This value’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.

The mean, or average, is found by summing all the numbers in a set and dividing by the total number of values. In this case, 5 + 10 + 15 + 20 + 25 = 75. Since there are 5 numbers, we divide 75 by 5, resulting in a mean of 15.

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.

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.

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.