how much does the mean score tell you about the performance of the whole class?

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firmablogF · Accepted Answer

Step 1
Averages are tools of summarizing data, it facilitates the comparison. Different averages are suitable to different situations are to be used.
Mean or arithmetic mean is most commonly used and widely applicable average.
Considering the situation as, there is class with 50 students. One test is conducted in the class. While reporting the score of class it is lengthy method to write each and every student’s score. To represent score of the class as a single unit mean is used.
Mean of the data can be calculated as:

\bar{X} = \frac{\sum x_{i}}{n}

Step 2
Mean is widely used due to its some good requisites,
Mean is easy to calculate and simple to follow.
It is based on all observations.
Mean is capable of further mathematical treatment. (as mean and sizes of more than two groups is given combined mean can be calculated)
If data is considered as 38, 43, 41, 39, 52, 48, 60, 167, mean of the data is 61.
Here among 8 observations 7 are smaller than mean.
Calculating mean is applicable for quantitative data only.
It is unduly affected by extreme observations and mean cannot be calculated graphically.
Hence, mean is not good average in all cases.

how much does the mean score tell you about the performance of the whole class?

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