5. On a randomly chosen day, each of the 32 students in a class recorded the time, \(t\) minutes to the nearest minute, they spent on their homework. The data for the class is summarised in the following table.
| Time, \(t\) | Number of students |
| 10-19 | 2 |
| 20-29 | 4 |
| 30-39 | 8 |
| 40-49 | 11 |
| 50-69 | 5 |
| 70-79 | 2 |
- Use interpolation to estimate the value of the median.
Given that
$$\sum t = 1414 \quad \text { and } \quad \sum t ^ { 2 } = 69378$$
- find the mean and the standard deviation of the times spent by the students on their homework.
- Comment on the skewness of the distribution of the times spent by the students on their homework. Give a reason for your answer.