NSC Mathematical Literacy Classifying and organising data: 3.1 Staff at public schools a

Question

3.1    Staff at public schools are required to adhere to stipulated percentages or fractions related to the total number of weekly periods based on their post level.

Table 5 below shows the stipulated teaching time per post level per school type.

TABLE 5: STIPULATED TEACHING TIME PER POST LEVEL PER SCHOOL TYPE

STAFF                     PRIMARY SCHOOL (PS)               SECONDARY SCHOOL (SS)
Post level 1 (teacher)      Between 85% and 92%             Between 85% and 90%
Post level 2 (departmental head)      3                                  3
Deputy principal                  3                                  6
Principal                           Between 10% and 92%              Between 5% and 60%

[Adapted from www.gov.za]

Woodhill Senior Secondary School (SS) has a timetable with 40 periods per week. The missing value, D, represents the number of periods taught by the deputy principal.

3  3  8  3  6  5  9  3  7  5  
10  23  27  29
31  31  31  32  32  36

Moloto Primary School (PS) has a timetable with 37 periods per week. Shown below are the number of periods per week allocated to the staff members.

3  9  10  10  10  11  12
15  15  15  15  18  19  
21  23  29  29

3.1.1    Determine the number of staff members at Woodhill SS.
3.1.2    Write down the modal number of periods per week for Moloto PS.
3.1.3    Calculate missing value D.
3.1.4    Ina stated that since the calculated mean for Woodhill SS is 33, the median would be a better reflection of the average number of periods taught per staff member.
Justify Ina’s statement with calculations.
3.1.5    Determine, as a fraction, the probability of randomly selecting a staff member at Moloto PS who teaches 29 or more periods per week.

3.2    TABLE 6A below shows the percentages achieved in Term 1 by ten selected learners of Woodhill SS for Task 1 and Task 2 in Mathematical Literacy.

TABLE 6A: PERCENTAGES ACHIEVED BY TEN SELECTED LEARNERS

LEARNER        A    B    C    D    E    F    G    H    I    J
Task 1        71  79  68  50  47  61  55  50  53  60
Task 2        53  69  53  49  50  47  61  15  47  81

On the ANSWER SHEET provided, the performances of Learners A to J for both tasks are plotted on a graph.

Use TABLE 6A and the graph on the ANSWER SHEET to answer the questions that follow.

3.2.1    (a)    Name the type of graph shown on the ANSWER SHEET.
(b)    Calculate the range of the percentages achieved for Task 2.
(c)    Identify the learner whose marks for both tasks can be classified as an outlier. Give a reason for your answer.

3.2.2    The school’s subject policy states that the difference between the mean of the two tasks should be below 15%.

The mean for Task 1 is calculated as 66,7%.

A teacher claimed that the difference in the mean mark for both tasks falls within the school’s subject policy statement.
Verify, showing all calculations, whether this teacher’s claim is VALID.

3.2.3    The achievements of two other selected learners, K and L, were added to TABLE 6A to create TABLE 6B.

TABLE 6B: PERCENTAGES ACHIEVED BY TWELVE SELECTED LEARNERS

LEARNER     A    B    C    D    E    F    G    H    I    J    K    L
Task 1      71   79  68  50  47  61  55  50  53  60  78  79
Task 2      53   69  53  49  50  47  61  15  47  81  36  45

Use the ANSWER SHEET provided, plot the results of Learner K and L for both tasks. Clearly label the plotted points, K and L.

3.1 Staff at public schools are required to adhere to stipulated percentages or fractions related to the total number of weekly periods based on their post level - NSC Mathematical Literacy - Question 3 - 2024 - Paper 1

Worked Solution & Example Answer:3.1 Staff at public schools are required to adhere to stipulated percentages or fractions related to the total number of weekly periods based on their post level - NSC Mathematical Literacy - Question 3 - 2024 - Paper 1

3.1.1 Determine the number of staff members at Woodhill SS.

3.1.2 Write down the modal number of periods per week for Moloto PS.

3.1.3 Calculate missing value D.

3.1.4 Justify Ina’s statement with calculations.

3.1.5 Determine, as a fraction, the probability of randomly selecting a staff member at Moloto PS who teaches 29 or more periods per week.

3.2.1 (a) Name the type of graph shown on the ANSWER SHEET.

3.2.1 (b) Calculate the range of the percentages achieved for Task 2.

3.2.1 (c) Identify the learner whose marks for both tasks can be classified as an outlier. Give a reason for your answer.

3.2.2 Verify, showing all calculations, whether this teacher’s claim is VALID.

3.2.3 Plotting the results of Learner K and L for both tasks.

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