Let's solve the problem step-by-step based on the given data in the table:

a) Berdasarkan Jadual 4 di atas, tentukan:

i) Kelas mod

The modal class is the class with the highest frequency.

From the table:

• Frequencies: 3, 1, 7, 12, 5, 2

The highest frequency is 12, which corresponds to the class 40–49.
Answer: 40–49

ii) Saiz selang kelas

The class size is calculated as the difference between the upper and lower boundaries of any class.

For example, the first class:

• Lower boundary: 10
• Upper boundary: 19

Class size = 19 - 10 + 1 = 10.

Answer: 10

iii) Julat

The range is the difference between the highest and lowest scores.

From the table:

• Lowest boundary: 10 (from the first class)
• Highest boundary: 69 (from the last class)

Range = 69 - 10 = 59.

Answer: 59

b) Berdasarkan Jadual 4 di atas, tanpa melukis ogif, hitungkan median.

The median can be calculated using the formula: $\text{Median} = L + \left( \frac{\frac{N}{2} - CF}{f} \right) \times C$

Where:

• $L$: Lower boundary of the median class
• $N$: Total frequency
• $CF$: Cumulative frequency before the median class
• $f$: Frequency of the median class
• $C$: Class size

Step 1: Find $N$ (Total frequency)

$N = 3 + 1 + 7 + 12 + 5 + 2 = 30$

Step 2: Locate the median class

The median class contains the $\frac{N}{2} = \frac{30}{2} = 15$-th value.

From the cumulative frequencies:

• 10–19: 3
• 20–29: $3 + 1 = 4$
• 30–39: $4 + 7 = 11$
• 40–49: $11 + 12 = 23$

The 15th value lies in the class 40–49.

Step 3: Apply the formula

For the class 40–49:

• $L = 40$ (lower boundary)
• $CF = 11$ (cumulative frequency before the class)
• $f = 12$ (frequency of the class)
• $C = 10$ (class size)

Substitute into the formula: $\text{Median} = 40 + \left( \frac{15 - 11}{12} \right) \times 10$ $\text{Median} = 40 + \left( \frac{4}{12} \right) \times 10$ $\text{Median} = 40 + \left( 0.333 \right) \times 10$ $\text{Median} = 40 + 3.33 = 43.33$

Answer: 43.33

Let me know if you need further clarification!
Here are 5 related questions to deepen your understanding:

1. How do we determine the mode for grouped data if two classes have the same highest frequency?
2. Why is it important to calculate the median instead of just using the mean in certain datasets?
3. Can the range alone give us a good understanding of data spread? Why or why not?
4. How would the calculations change if the class intervals were not equal?
5. How do cumulative frequencies help in determining the median?

Tip: Always organize cumulative frequency tables carefully to avoid mistakes in finding the median class.