Question

1. for the following set of scores:

6 3 7 6 1 2 7 3 6 4
1 2 4 7 4 4 5 5 6 6
(a) construct a frequency distribution table to organize the scores. include cumulative frequency and cumulative percent.

Explanation:

Step1: Identify unique scores

First, we list out the unique scores from the given data. The scores are: 1, 2, 3, 4, 5, 6, 7.

Step2: Count frequency of each score

Now we count how many times each score appears:

• Score 1: Appears 2 times.
• Score 2: Appears 2 times.
• Score 3: Appears 2 times.
• Score 4: Appears 4 times.
• Score 5: Appears 2 times.
• Score 6: Appears 5 times.
• Score 7: Appears 3 times.

Step3: Calculate cumulative frequency

Cumulative frequency is the sum of frequencies up to that score.

• For score 1: Cumulative frequency = 2
• For score 2: Cumulative frequency = 2 + 2 = 4
• For score 3: Cumulative frequency = 4 + 2 = 6
• For score 4: Cumulative frequency = 6 + 4 = 10
• For score 5: Cumulative frequency = 10 + 2 = 12
• For score 6: Cumulative frequency = 12 + 5 = 17
• For score 7: Cumulative frequency = 17 + 3 = 20 (Total number of scores is 2 + 2 + 2 + 4 + 2 + 5 + 3 = 20)

Step4: Calculate cumulative percent

Cumulative percent is calculated as $\frac{\text{Cumulative Frequency}}{\text{Total Number of Scores}} \times 100$.

• For score 1: $\frac{2}{20} \times 100 = 10\%$
• For score 2: $\frac{4}{20} \times 100 = 20\%$
• For score 3: $\frac{6}{20} \times 100 = 30\%$
• For score 4: $\frac{10}{20} \times 100 = 50\%$
• For score 5: $\frac{12}{20} \times 100 = 60\%$
• For score 6: $\frac{17}{20} \times 100 = 85\%$
• For score 7: $\frac{20}{20} \times 100 = 100\%$

Step5: Construct the frequency distribution table

We organize the data into a table with columns: Score, Frequency, Cumulative Frequency, Cumulative Percent.

Score	Frequency	Cumulative Frequency	Cumulative Percent
2	2	4	20%
3	2	6	30%
4	4	10	50%
5	2	12	60%
6	5	17	85%
7	3	20	100%

Answer:

The frequency distribution table is as shown above:

Score	Frequency	Cumulative Frequency	Cumulative Percent
2	2	4	20%
3	2	6	30%
4	4	10	50%
5	2	12	60%
6	5	17	85%
7	3	20	100%