The table shows the distribution of the number of hours per day spent in studying by 50 students. Number of hours per day 4 5 6 7 8 9 10 11 Number of studen...

Answer Details

Given distribution.

Total number of students: \(\sum f = 50\).

(a) Mean. Compute \(\sum fx\):

\[\sum fx = 20+35+30+63+96+36+30+55 = 365.\]

\[\bar{x} = \frac{\sum fx}{\sum f} = \frac{365}{50} = 7.30.\]

(b) Standard deviation. Compute \(\sum fx^{2}\):

\[\sum fx^{2} = 80+175+180+441+768+324+300+605 = 2873.\]

\[\text{Variance} = \frac{\sum fx^{2}}{\sum f} - \bar{x}^{2} = \frac{2873}{50} - (7.3)^{2} = 57.46 - 53.29 = 4.17.\]

\[\text{S.D.} = \sqrt{4.17} = 2.04 \text{ (2 d.p.).}\]

The mean study time is 7.30 hours and the standard deviation is 2.04 hours.