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,

l.m.m.k, let's knock this out. 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 | (0+10)/(2) = 5 | 5 × 5 = 25 | | 11-20 | 18 | (11+20)/(2) = 15.5 | 18 × 15.5 = 279 | | 21-30 | 32 | (21+30)/(2) = 25.5 | 32 × 25.5 = 816 | | 31-40 | 25 | (31+40)/(2) = 35.5 | 25 × 35.5 = 887.5 | | 41-50 | 10 | (41+50)/(2) = 45.5 | 10 × 45.5 = 455 | | Total | f = 90 | | fx = 2462.5 | Step 2: Calculate the mean using the formula Mean = ( fx)/( f). Mean = (2462.5)/(90) Mean = 27.3611... Step 3: Round the mean to two decimal places. 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 | |||| |||| | 8 | | 15-19 | |||| || | 7 | | 20-24 | |||| |||| | 8 | | 25-29 | |||| | | 5 | | 30-34 | |||| || | 7 | | 35-39 | |||| || | 7 | | Total | | 42 | The completed frequency distribution table is: |c|c| Time (minutes) & Frequency \\ 10-14 & 8 \\ 15-19 & 7 \\ 20-24 &