Problem: The following table represents the number of hours spent by a group of students studying for an exam:

Hours Studied	Number of Students
0-2	5
2-4	8
4-6	12
6-8	10
8-10	7
10-12	4
12-14	2

Find the mean and standard deviation of the number of hours studied.

Solution: To find the mean, we need to calculate the midpoint of each class interval and multiply it by the corresponding frequency. Then, we sum up these products and divide by the total number of students.

Hours Studied	Midpoint	Number of Students	Frequency x Midpoint
0-2	1	5	5
2-4	3	8	24
4-6	5	12	60
6-8	7	10	70
8-10	9	7	63
10-12	11	4	44
12-14	13	2	26
Total		48	292

The sum of the frequency x midpoint is 292. Since there are 48 students in total, the mean is 292/48 = 6.08 hours.

To find the standard deviation, we need to calculate the squared deviation from the mean for each class interval, multiply it by the corresponding frequency, and sum up these products. Then, we divide by the total number of students and take the square root.

Hours Studied	Midpoint	Number of Students	Deviation from Mean (x - 6.08)	(x - 6.08)^2	Frequency x (x - 6.08)^2
0-2	1	5	-5.08	25.8064	129.032
2-4	3	8	-3.08	9.4864	75.8912
4-6	5	12	-1.08	1.1664	13.9968
6-8	7	10	0.92	0.8464	8.464
8-10	9	7	2.92	8.5264	59.6848
10-12	11	4	4.92	24.2064	96.8256
12-14	13	2	6.92	47.8464	95.6928
Total		48		117.9384	479.5776

The sum of the frequency x (x - 6.08)^2 is 479.5776. Since there are 48 students in total, the variance is 479.5776/48 = 9.9912. Taking the square root of the variance, the standard deviation is √9.9912 = 3.16 hours.