To solve for the first quartile (Q1) from the data shown in the graph, let's follow these steps:

Step 1: Identify the data points

The graph represents a frequency distribution with the x-axis as categories and the y-axis representing the frequency ("Banyak Siswa"). Each x-value represents a particular group or category.

• For $x = 4$, $y = 3$
• For $x = 5$, $y = 4$
• For $x = 6$, $y = 4$
• For $x = 7$, $y = 8$
• For $x = 8$, $y = 10$
• For $x = 9$, $y = 5$
• For $x = 10$, $y = 2$

These represent the frequency of students for each category.

Step 2: Compute the cumulative frequency

To find the quartiles, we need the cumulative frequency:

• Cumulative frequency for $x = 4$: 3
• Cumulative frequency for $x = 5$: 3 + 4 = 7
• Cumulative frequency for $x = 6$: 7 + 4 = 11
• Cumulative frequency for $x = 7$: 11 + 8 = 19
• Cumulative frequency for $x = 8$: 19 + 10 = 29
• Cumulative frequency for $x = 9$: 29 + 5 = 34
• Cumulative frequency for $x = 10$: 34 + 2 = 36

Step 3: Calculate the position of Q1

The first quartile (Q1) is located at 25% of the cumulative frequency. Since the total cumulative frequency is 36: $Q1 \text{ position} = \frac{1}{4} \times 36 = 9$

Step 4: Determine Q1 value

Looking at the cumulative frequency table, the value corresponding to the 9th position is at $x = 7$ since:

• At $x = 6$, the cumulative frequency is 11, so Q1 is located in this category.

Thus, the first quartile (Q1) is at $x = 6$.

Do you want further details on this, or have any questions?
Here are 5 related questions to enhance your understanding:

1. What are the steps to calculate the second quartile (median) from this data?
2. How is the third quartile (Q3) calculated using a similar process?
3. How does the cumulative frequency distribution help in finding quartiles?
4. What other measures of spread can be calculated from a frequency distribution?
5. How would the quartiles change if the data had outliers?

Tip: Always ensure your data is sorted when calculating quartiles to avoid mistakes.