Question

1. Given the data below, calculate the mean, calculate the standard deviation and explain the significance of each in the context of the data.

Grade on Final Exam	Frequency
50	1
60	2
70	3
80	5
90	6
100	3

Answer 1

Given is a data on grade on final exam, here we need to determine the mean and standard deviation for the given data.

The data is,

No.	Grade on Final Exam(xi)	Frequency(fi)
1	50	1
2	60	2
3	70	3
4	80	5
5	90	6
6	100	3

Mean

The mean is a measure of central tendency and the mean gives a fair idea about the value around which the data is clustered. It is given by,

Standard Deviation

The standard deviation gives the measure of spread of the data or how dispersed or data is. It is given by,

Coming back to our problem,

No.	Grade on Final Exam(xi)	Frequency(fi)	xi*fi	((xi-x̄)^2)*fi
1	50	1	50	961
2	60	2	120	882
3	70	3	210	363
4	80	5	400	5
5	90	6	540	486
6	100	3	300	1083
Total		20	1620	3780

The Mean is,

The Standard Deviation is,