The table shows marks scored by students: a) Calculate the mean mark. b) The table below shows time in minutes that a group of 45 students took to complete a mathematics test. i) From the given data,

6. The table shows marks scored by students:

a) Calculate the mean mark.

Step 1: Determine the midpoint ($x$) for each class interval and calculate $fx$.

Marks	Frequency ($f$)	Midpoint ($x$)	$fx$
0-10	5	$\frac{0+10}{2} = 5$	$5 \times 5 = 25$
11-20	18	$\frac{11+20}{2} = 15.5$	$18 \times 15.5 = 279$
21-30	32	$\frac{21+30}{2} = 25.5$	$32 \times 25.5 = 816$
31-40	25	$\frac{31+40}{2} = 35.5$	$25 \times 35.5 = 887.5$
41-50	10	$\frac{41+50}{2} = 45.5$	$10 \times 45.5 = 455$
Total	$\sum f = 90$		$\sum fx = 2462.5$

Step 2: Calculate the mean using the formula $\text{Mean} = \frac{\sum fx}{\sum f}$.

$$\text{Mean} = \frac{2462.5}{90}$$ $$\text{Mean} = 27.3611...$$

Step 3: Round the mean to two decimal places.

$$\boxed{\text{Mean} = 27.36}$$

b) The table below shows time in minutes that a group of 45 students took to complete a mathematics test.

i) From the given data, complete the frequency distribution table below.
The given data points are:
10, 25, 24, 22, 35, 17, 32, 30, 13, 21, 16, 34, 13
35, 22, 28, 26, 13, 14, 32, 37, 20, 27, 22, 17, 35, 20
37, 38, 15, 16, 14, 32, 34, 28, 11, 31, 13, 22, 15, 38, 19

Step 1: Count the number of data points. There are 42 data points provided. (Note: The question states "a group of 45 students", but only 42 data points are given. The table will be based on the 42 provided data points.)

Step 2: Create class intervals and tally the frequencies. We will use class intervals of 5 minutes, starting from 10.

Time (minutes)	Tally	Frequency ($f$)
10-14	$\text{								}$	8
15-19	$\text{						}$	7
20-24	$\text{								}$	8
25-29	$\text{					}$	5
30-34	$\text{						}$	7
35-39	$\text{						}$	7
Total		42

The completed frequency distribution table is:

$$$$