What is a mode, mean, median, range?
Give examples of each
Mode, mean, median, and range are measures of central tendency and dispersion used in statistics to describe the characteristics of a dataset.
1. Mode: The mode is the value that appears most frequently in a dataset. A dataset can have more than one mode if multiple values appear with the same highest frequency.
Example: In the dataset {2, 3, 4, 4, 5, 7, 7, 7, 9}, the mode is 7 because it appears the most times (3 times).
2. Mean: The mean, also known as the average, is the sum of all the values in a dataset divided by the number of values.
Example: For the dataset {2, 3, 4, 4, 5, 7, 7, 7, 9}, the mean is (2 + 3 + 4 + 4 + 5 + 7 + 7 + 7 + 9)/9 = 48/9 = 5.33.
3. Median: The median is the middle value of a dataset when the values are arranged in ascending or descending order. If there is an even number of values, the median is the average of the middle two values.
Example: In the dataset {2, 3, 4, 4, 5, 7, 7, 7, 9}, the median is 5 because it is the middle value. If the dataset were {2, 3, 4, 4, 5, 7, 7, 7}, the median would be (4 + 5)/2 = 4.5 because there is an even number of values.
4. Range: The range is the difference between the highest and lowest values in a dataset.
Example: For the dataset {2, 3, 4, 4, 5, 7, 7, 7, 9}, the range is 9 - 2 = 7.
In summary, for the dataset {2, 3, 4, 4, 5, 7, 7, 7, 9}, the mode is 7, the mean is 5.33, the median is 5, and the range is 7.