Mean marks obtained by 100 students are estimated to be 80 . Later on ...
Calculation of the Corrected Mean
Given:
- Number of students (n) = 100
- Mean marks obtained by 100 students (x) = 80
- One value was incorrectly read as 86 instead of 26
To find the corrected mean, we need to first find the sum of all the marks obtained by the students:
Sum of marks obtained by 100 students = n * x = 100 * 80 = 8000
We know that one value was read as 86 instead of 26. Let's correct this error:
Corrected sum of marks = 8000 - 86 + 26 = 7940
Now, we can find the corrected mean:
Corrected mean = Corrected sum of marks / n = 7940 / 100 = 79.4
Explanation
In statistics, mean is a measure of central tendency. It represents the average of a set of data. In this question, we are given the mean marks obtained by 100 students as 80. However, we are also told that one value was read incorrectly as 86 instead of 26. This means that the sum of marks obtained by the students was calculated incorrectly.
To find the corrected mean, we need to first find the correct sum of marks. We can do this by subtracting the incorrect value (86) and adding the correct value (26) to the sum of marks. Once we have the correct sum of marks, we can divide it by the number of students to get the corrected mean.