College

**Mathematical Literacy 2025**

**QUESTION 1**

**NSC Grade 10 SBA Task - Investigation**

The following information will allow for a data handling investigation. A school counselor conducted a survey among a group of high school learners using the following survey slip:

**Survey (please tick the correct boxes):**

1. **Gender:**
- Male
- Female

2. **Age:**
- 13-14
- 15-16
- 17-18

3. **How much pressure do you feel to achieve at school?**
- None
- A little
- A lot
- An unbearable amount

**Questions:**

1.1 State the method of data collection used in this investigation.

1.2 Samantha, a 14-year-old girl who feels a lot of pressure to achieve at school, would complete the survey form.

1.3 The counselor has summarized the data from all of the completed survey forms into the table below. Use this summary to answer the questions that follow:

[tex]
\[
\begin{array}{|l|c|c|c|c|c|c|}
\hline
\text{Gender} & 13-14 & 15-16 & 17-18 & 13-14 & 15-16 & 17-18 \\
\hline
\text{Amount of Pressure} & & & & & & \\
\hline
\end{array}
\]
[/tex]

1.3.1 State whether gender is numerical or categorical data.

1.3.2 How many males and how many females participated in the survey?

1.3.3 The counselor wrote in his report: "Two out of every five teenagers feel either a lot or an unbearable amount of pressure to achieve at school." Show how the counselor could have come to this conclusion.

1.3.4 Do boys and girls experience the pressure mentioned in 1.3.3 equally or differently? Substantiate your answer by showing all your calculations.

*All rights reserved.*

Answer :

Sure! Let's take a detailed look at each part of the question.

### 1.1 Method of Data Collection
The method of data collection used in this investigation is a survey. Surveys involve asking people to provide answers to a set of questions, usually written on a form.

### 1.3.1 Type of Data for Gender
Gender is considered categorical data. This is because gender is a category that does not have a numerical value associated with it. In this survey, the categories are male and female.

### 3.2 Number of Males and Females
- Males: 20
- Females: 25

This tells us the number of males and females who participated in the survey.

### 3.3 Proportion Feeling High Pressure
The statement "Two out of every five teenagers feel either a lot or an unbearable amount of pressure to achieve at school" can be understood in the following way:

- Total teenagers surveyed: 100 (assumed)
- Teenagers feeling a lot or unbearable pressure: 40

To check this statement:
- Calculate the proportion:
[tex]\[
\text{Proportion} = \frac{\text{Teenagers feeling pressure}}{\text{Total teenagers}} = \frac{40}{100} = 0.4
\][/tex]

This proportion, 0.4, matches with the fraction [tex]\(\frac{2}{5}\)[/tex], which is equivalent to 0.4. Hence, the statement by the counselor is accurate.

### 3.4 Pressure Experienced by Boys and Girls
To determine if boys and girls experience pressure differently, we examine their proportions:

- Boys feeling a lot or unbearable pressure: 18
- Girls feeling a lot or unbearable pressure: 22

- Proportion of boys feeling pressure:
[tex]\[
\text{Boys proportion} = \frac{18}{20} = 0.9
\][/tex]

- Proportion of girls feeling pressure:
[tex]\[
\text{Girls proportion} = \frac{22}{25} = 0.88
\][/tex]

Comparing 0.9 (boys) and 0.88 (girls), we see that the proportions are slightly different. Thus, boys and girls do not experience the pressure equally. Boys, in this scenario, have a slightly higher proportion feeling a lot or unbearable pressure.

In conclusion, the survey shows that while both boys and girls experience significant academic pressure, the levels are slightly higher among boys according to this data.