Let's work through the problem step-by-step.

We have a list of exam scores, and we're instructed to create a frequency table using 5-point bins, starting from the 90-94 range and moving upwards.

Given Scores:

76, 87, 83, 78, 91, 75, 99, 86, 83, 95, 70, 85, 93, 75, 90, 91, 93, 80, 89, 87

Bins:

• 95 to 99
• 90 to 94
• 85 to 89
• 80 to 84
• 75 to 79
• 70 to 74

Steps to Create the Frequency Table:

1. Frequency: Count how many scores fall into each bin.
2. Relative Frequency: Divide the frequency of each bin by the total number of scores, then multiply by 100 to convert to a percentage.
3. Cumulative Frequency: Add the frequencies in a running total from the lowest bin to the highest.

1. Frequency Count:

We count the scores falling into each bin:

• 95 to 99: 99, 95 → 2 scores
• 90 to 94: 91, 93, 91, 93, 90 → 5 scores
• 85 to 89: 87, 86, 85, 87, 89 → 5 scores
• 80 to 84: 83, 83, 80 → 3 scores
• 75 to 79: 76, 78, 75, 75 → 4 scores
• 70 to 74: 70 → 1 score

2. Relative Frequency:

Total number of scores = 20

For each bin:

• 95 to 99: (2/20) * 100 = 10%
• 90 to 94: (5/20) * 100 = 25%
• 85 to 89: (5/20) * 100 = 25%
• 80 to 84: (3/20) * 100 = 15%
• 75 to 79: (4/20) * 100 = 20%
• 70 to 74: (1/20) * 100 = 5%

3. Cumulative Frequency:

• 95 to 99: 2
• 90 to 94: 2 + 5 = 7
• 85 to 89: 7 + 5 = 12
• 80 to 84: 12 + 3 = 15
• 75 to 79: 15 + 4 = 19
• 70 to 74: 19 + 1 = 20

Completed Frequency Table:

Would you like more details or any further clarifications?

Related Questions:

1. How would the table change if we used different bin sizes (e.g., 10-point bins)?
2. What is the importance of cumulative frequency in understanding data distribution?
3. How does the choice of bin size affect the relative frequency distribution?
4. Can you create a histogram based on this frequency table?
5. What additional insights can we gain by analyzing the median or mode of this data?

Tip:

The cumulative frequency helps to quickly see how data accumulates across ranges, which is useful for percentile calculations.