Let's analyze the given dataset of mathematical scores for 40 students:

a. List of single data distribution (frequency distribution):

Score (x)	Frequency (f)
3	1
4	7
5	6
6	10
7	8
8	6
9	1
10	1

b. Mean (Average)

The formula for the mean is:

$\text{Mean} = \frac{\sum x_i f_i}{N}$

Where:

• $x_i$ is each score.
• $f_i$ is the frequency of each score.
• $N = 40$ is the total number of students.

Let's calculate the mean:

$\text{Mean} = \frac{(3 \times 1) + (4 \times 7) + (5 \times 6) + (6 \times 10) + (7 \times 8) + (8 \times 6) + (9 \times 1) + (10 \times 1)}{40}$

$\text{Mean} = \frac{3 + 28 + 30 + 60 + 56 + 48 + 9 + 10}{40} = \frac{244}{40} = 6.1$

The mean is 6.1.

c. Third Quartile (Q3)

The third quartile (Q3) is the value that separates the lowest 75% of the data from the highest 25%. For 40 students, Q3 is the score at the position:

$Q3 = \frac{3(N+1)}{4} = \frac{3(40+1)}{4} = \frac{123}{4} = 30.75$

So, Q3 is the 31st score. Let's arrange the data in ascending order:

$3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 10$

The 31st score is 7.

Thus, Q3 = 7.

d. Range (Jangkauan)

The range is the difference between the maximum and minimum values in the data set:

$\text{Range} = \text{Max} - \text{Min} = 10 - 3 = 7$

So, the range is 7.

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Would you like further details on any of these steps or have any questions?

Here are 5 related questions for you to explore:

1. How would you calculate the median (Q2) of this dataset?
2. Can you calculate the mode of the data, and what does it represent?
3. How do you calculate the variance and standard deviation for this dataset?
4. What would happen to the mean if the highest score was increased to 15?
5. How does the interquartile range (IQR) help in understanding the spread of the data?

Tip: Always double-check the data arrangement in ascending order when calculating quartiles!