**Question 1**:

The data below shows the age of 25 tourists who visited a tourist spot.

2 25 8 15 19 17 4 28 10 16 16 18 19 7 28 14 22 20 6 26 24 16 8 11 30 |

**(a)**Copy and complete the table below based on the data above.Age (years) |
Frequency |
Midpoint |

1 – 5 |
2 |
3 |

6 – 10 |
||

**(b)**Based on the completed table above,

**(i)**State the modal class.

**(ii)**Calculate the mean age of the tourists.

**(c)**

*For this part of the question, use graph paper.*

By using a scale of 2cm to 5 years on the horizontal axis and 2cm to 1

tourist on the vertical axis, draw a histogram for the data.

**:**

SolutionSolution

**(a)**

Age (years) |
Frequency |
Midpoint |

1 – 5 |
2 |
3 |

6 – 10 |
5 |
8 |

11 – 15 |
3 |
13 |

16 – 20 |
8 |
18 |

21 – 25 |
3 |
23 |

25 – 30 |
4 |
28 |

Calculation of midpoint for (age 6 – 10) = $\frac{6+10}{2}=8$

**(b)(i)**

Modal class = age 16 – 20 (highest frequency)

**(b)(ii)**

$$\begin{array}{l}\text{mean age =}\frac{3\times 2+8\times 5+13\times 3+18\times 8+23\times 3+28\times 4}{25}\\ \text{=}16.4\end{array}$$

**(c)**

**Question 2**:

Diagram below shows the marks, obtained by a group of 24 students in a mathematics quiz.

(a) Based on the data in diagram above, complete Table in the answer space.

(b) State the modal class.

(c) Calculate the estimated marks obtained by a student.

(d)

*For this part of the question, use graph paper.*

By using a scale of 2cm to 5 marks on the horizontal axis and 2cm to 1 student on the vertical axis, draw a histogram for the data.

(e) Based on the histogram drawn in (d), state the number of students who obtain less than 32 marks in the quiz.

*Answer:*

**:**

SolutionSolution

**(a)**

**(b)**Modal class = 27 – 31 (highest frequency)

$\begin{array}{l}\text{(c)}\\ \text{Estimatedmean}\\ \text{=}\frac{4\times 24+7\times 29+6\times 34+4\times 39+2\times 44+1\times 49}{24}\\ \text{=}\frac{796}{24}\\ =33.17\text{marks}\end{array}$

**(d)**

**Number of students who obtained less than 32 marks**

(e)

(e)

= 4 + 7

= 11