Find the mean, median, and mode for the following data set: 26, 19, 55, 27, 14, 18, 26, 10, 42, 40, 33, and five.
In order to calculate the mean of a data set, we divide the sum of the values by the number of values. Adding the values in our data set gives us a total of 315. There are 12 values altogether, so we need to divide 315 by 12 to calculate the mean. This is equal to 26.25.
The median is the middle value when our numbers are in ascending or descending order. The smallest number in our list is five. This is followed by 10. The remaining numbers in order are 14, 18, 19, 26, 26, 27, 33, 40, 42, and 55. When dealing with a small data set like this, we can find the middle value by crossing off one from either end. In this case, we cross off 55 and five.
We can repeat this process by crossing off the next four highest and next four lowest numbers. As we have an even number of values, there are two middle numbers. If these were different, the median would be the midpoint of the two values. In this case, as they are both 26, the median is 26.
The mode is the most frequently occurring value. It is the number that appears the most. In this data set, all of the values appear once with the exception of 26 which appears twice. Therefore, 26 is the mode. The mean, median, and mode of this data set are 26.25, 26, and 26, respectively.