If you were a teacher, and these numbers represented your students' scores on a test, would the median or mean give a better picture of the overall class performance?
The numbers are 22,38,42,65,75,76,79,82,83,87,88,89,89,91,92,94,96,97,98
The mean is: 78.053 & the median is: 87
Could someone also explain the answer please!!
22,38, pull the mean down terribly because those two students were out with the flu or something. Therefore the median is more useful. The majority of the students were up in the eighties and above.
To determine whether the median or mean gives a better picture of the overall class performance, we need to understand the characteristics of both measures.
The mean, also known as the average, is calculated by adding up all the numbers in a dataset and then dividing by the total number of values. It provides a measure of central tendency that is influenced by extreme values. If there are outliers in the dataset, they can significantly impact the mean.
The median is the middle value when the data is arranged in ascending or descending order. It is not affected by extreme values or outliers. This makes it a robust measure of central tendency.
In this case, the mean of the scores is 78.053, while the median is 87. Since the median is less affected by extreme values, it gives a better representation of the typical performance of students in the class.
To calculate the mean, you would add up all the numbers in the dataset (22 + 38 + 42 + 65 + 75 + 76 + 79 + 82 + 83 + 87 + 88 + 89 + 89 + 91 + 92 + 94 + 96 + 97 + 98 = 1485) and then divide by the total number of values (19). The mean is 78.053.
To calculate the median, you need to arrange the numbers in ascending or descending order. After arranging the numbers, you find the middle value, which is 87 in this case.
Therefore, the median (87) provides a better representation of the overall class performance compared to the mean (78.053).