一组学生被要求完成一次课堂测试。完成测试所花费的时间如以下表格所示：

1. Find the position of the median value and locate it using cumulative frequencies.

Total number of students:

$12+49+81+33+25=200$

The median lies between the $100$th and $101$st values.

Cumulative frequencies:

$12,\ 12+49=61,\ 61+81=142$

Since the $100$th and $101$st values lie in the class where the cumulative frequency reaches $142$, the median class is $45 < x \leqslant 55$.

1. State the effect on the mean when every student's time increases by 5 minutes.

Each time value becomes $x+5$.

Therefore the mean also increases by $5$ minutes.

2. State the effect on the standard deviation when every data value is increased by the same amount.

Adding $5$ minutes to every time value does not change the differences of the values from the mean.

Hence the spread of the data is unchanged, so the standard deviation remains the same.