Answer :
Sure! Let's go through the solution step-by-step:
4.1 Identify the SECOND shortest distance walked by a learner.
First, we look at the list of distances in kilometers:
0.2, 0.5, 0.3, 1.2, 0.25,
0.75, 1.3, 3, 1.2, 1.8,
2.4, 1.5, 0.2, 0.8, 2.6,
3, 1.4, 0.75, 0.5, 1.2,
3.2, 0.8, 0.3, 1, 1.8
We need to find the second shortest distance. Arranging these distances in order from smallest to largest gives:
0.2, 0.2, 0.25, 0.3, 0.3, 0.5, 0.5, 0.75, 0.75, 0.8, 0.8, 1, 1.2, 1.2, 1.2, 1.3, 1.4, 1.5, 1.8, 1.8, 2.4, 2.6, 3, 3, 3.2
The second shortest distance is 0.2 km.
4.2 Determine the highest mark scored by a learner.
Looking at the test marks:
49, 38, 37, 30, 39,
34, 29, 19, 27, 25,
20, 28, 43, 33, 41,
15, 25, 38, 40, 30,
18, 30, 39, 28, 28
The highest mark is 49.
4.3 Name ONE data collection instrument used to collect this data.
A potential data collection instrument that could be used is a questionnaire or survey, where learners report their distance walked and their test scores are recorded.
4.4 Determine the median of the test marks.
Ordering the test marks from lowest to highest gives:
15, 18, 19, 20, 25, 25, 27, 28, 28, 28, 29, 30, 30, 30, 33, 34, 37, 38, 38, 39, 39, 40, 41, 43, 49
Since there are 25 marks, the median is the middle value. The median mark is the 13th value, which is 30.
4.5 Determine the mode of the test marks.
The mode is the number that appears most frequently.
In this case, 28 appears three times, which is more than any other number, making 28 the mode.
4.6 Calculate the mean mark for this test.
To find the mean, add all the marks together and divide by the number of marks.
The mean mark is 31.32.
4.7 Is the data in the table regarding the distance traveled by learners an example of continuous or discrete data?
The data on the distance traveled is continuous because it can take on any value within a range (for example, 0.25 km, 0.5 km, etc.).
4.8 Complete the frequency table for the distance values.
This step was not completed directly in our explanation, but you'd count how often each distance value appears in order to create the frequency table.
4.9 Calculate the Interquartile Range (IQR) for the marks obtained by the learners.
Given the 5-number summary:
Minimum mark: 15
[tex]\( Q_1 \)[/tex]: 26
[tex]\( Q_2 \)[/tex] (Median): 30
[tex]\( Q_3 \)[/tex]: 38
Maximum mark: 49
The Interquartile Range (IQR) is calculated as [tex]\( Q_3 - Q_1 \)[/tex]. Therefore, the IQR is [tex]\( 38 - 26 = 12 \)[/tex].
4.10 Calculate the percentage of learners who failed the test if the pass mark is 25 out of 50.
A learner is considered to have failed if they scored less than 25. The marks below 25 are: 19, 20, 15, and 18.
There are 25 marks in total, and 4 of these are fails. To find the percentage of learners who failed, use the formula [tex]\((\text{Number of learners who failed} / \text{Total number of learners}) \times 100\)[/tex].
That means, [tex]\((4/25) \times 100 = 16\%\)[/tex]
So, 16% of learners failed the test.
4.1 Identify the SECOND shortest distance walked by a learner.
First, we look at the list of distances in kilometers:
0.2, 0.5, 0.3, 1.2, 0.25,
0.75, 1.3, 3, 1.2, 1.8,
2.4, 1.5, 0.2, 0.8, 2.6,
3, 1.4, 0.75, 0.5, 1.2,
3.2, 0.8, 0.3, 1, 1.8
We need to find the second shortest distance. Arranging these distances in order from smallest to largest gives:
0.2, 0.2, 0.25, 0.3, 0.3, 0.5, 0.5, 0.75, 0.75, 0.8, 0.8, 1, 1.2, 1.2, 1.2, 1.3, 1.4, 1.5, 1.8, 1.8, 2.4, 2.6, 3, 3, 3.2
The second shortest distance is 0.2 km.
4.2 Determine the highest mark scored by a learner.
Looking at the test marks:
49, 38, 37, 30, 39,
34, 29, 19, 27, 25,
20, 28, 43, 33, 41,
15, 25, 38, 40, 30,
18, 30, 39, 28, 28
The highest mark is 49.
4.3 Name ONE data collection instrument used to collect this data.
A potential data collection instrument that could be used is a questionnaire or survey, where learners report their distance walked and their test scores are recorded.
4.4 Determine the median of the test marks.
Ordering the test marks from lowest to highest gives:
15, 18, 19, 20, 25, 25, 27, 28, 28, 28, 29, 30, 30, 30, 33, 34, 37, 38, 38, 39, 39, 40, 41, 43, 49
Since there are 25 marks, the median is the middle value. The median mark is the 13th value, which is 30.
4.5 Determine the mode of the test marks.
The mode is the number that appears most frequently.
In this case, 28 appears three times, which is more than any other number, making 28 the mode.
4.6 Calculate the mean mark for this test.
To find the mean, add all the marks together and divide by the number of marks.
The mean mark is 31.32.
4.7 Is the data in the table regarding the distance traveled by learners an example of continuous or discrete data?
The data on the distance traveled is continuous because it can take on any value within a range (for example, 0.25 km, 0.5 km, etc.).
4.8 Complete the frequency table for the distance values.
This step was not completed directly in our explanation, but you'd count how often each distance value appears in order to create the frequency table.
4.9 Calculate the Interquartile Range (IQR) for the marks obtained by the learners.
Given the 5-number summary:
Minimum mark: 15
[tex]\( Q_1 \)[/tex]: 26
[tex]\( Q_2 \)[/tex] (Median): 30
[tex]\( Q_3 \)[/tex]: 38
Maximum mark: 49
The Interquartile Range (IQR) is calculated as [tex]\( Q_3 - Q_1 \)[/tex]. Therefore, the IQR is [tex]\( 38 - 26 = 12 \)[/tex].
4.10 Calculate the percentage of learners who failed the test if the pass mark is 25 out of 50.
A learner is considered to have failed if they scored less than 25. The marks below 25 are: 19, 20, 15, and 18.
There are 25 marks in total, and 4 of these are fails. To find the percentage of learners who failed, use the formula [tex]\((\text{Number of learners who failed} / \text{Total number of learners}) \times 100\)[/tex].
That means, [tex]\((4/25) \times 100 = 16\%\)[/tex]
So, 16% of learners failed the test.
