Question

use 6-point bins (94 to 99, 88 to 93, etc.) to make a frequency table for the set of exam scores shown below. include columns for relative frequency and cumulative frequency.

69 99 81 93 93 65 83 95 88 97 73 99 98 90 79 98 79 86 64 78

complete the frequency table below.

scores frequency relative frequency cumulative frequency
94 to 99
88 to 93
82 to 87
76 to 81
70 to 75
64 to 69
total

Explanation:

Sort and count data into bins

The given dataset of 20 exam scores is:
\(69, 99, 81, 93, 93, 65, 83, 95, 88, 97, 73, 99, 98, 90, 79, 98, 79, 86, 64, 78\)

Total number of data points \(N = 20\).

We count the frequency for each 6-point bin:

• 94 to 99: \(99, 95, 97, 99, 98, 98\) \(

ightarrow\) Frequency = \(6\)

• 88 to 93: \(93, 93, 88, 90\) \(

ightarrow\) Frequency = \(4\)

• 82 to 87: \(83, 86\) \(

ightarrow\) Frequency = \(2\)

• 76 to 81: \(81, 79, 79, 78\) \(

ightarrow\) Frequency = \(4\)

• 70 to 75: \(73\) \(

ightarrow\) Frequency = \(1\)

• 64 to 69: \(69, 65, 64\) \(

ightarrow\) Frequency = \(3\)

Total Frequency = \(6 + 4 + 2 + 4 + 1 + 3 = 20\).

Calculate relative frequencies

Relative frequency is calculated as \(\frac{\text{Frequency}}{N} \times 100\%\):

• 94 to 99: \(\frac{6}{20} \times 100\% = 30\%\)
• 88 to 93: \(\frac{4}{20} \times 100\% = 20\%\)
• 82 to 87: \(\frac{2}{20} \times 100\% = 10\%\)
• 76 to 81: \(\frac{4}{20} \times 100\% = 20\%\)
• 70 to 75: \(\frac{1}{20} \times 100\% = 5\%\)
• 64 to 69: \(\frac{3}{20} \times 100\% = 15\%\)
• Total: \(100\%\)

Calculate cumulative frequencies

Cumulative frequency is the running total of frequencies from the highest score bin down to the lowest score bin:

• 94 to 99: \(6\)
• 88 to 93: \(6 + 4 = 10\)
• 82 to 87: \(10 + 2 = 12\)
• 76 to 81: \(12 + 4 = 16\)
• 70 to 75: \(16 + 1 = 17\)
• 64 to 69: \(17 + 3 = 20\)

Answer:

Scores	Frequency	Relative Frequency	Cumulative Frequency
88 to 93	4	20%	10
82 to 87	2	10%	12
76 to 81	4	20%	16
70 to 75	1	5%	17
64 to 69	3	15%	20
Total	20	100%