# 8.3.2. Ascending and Descending Cumulative Frequency Tables and Their Graphical Representation

The table below shows the frequency distribution of the grades of 60 students in an exam. Find the number of failed students, given that the minimum success grade is 30 marks.

 Sets Total Frequency 60 0– 10– 20– 30– 40– 50– 3 18 10 8 15 6

• A31 students
• B10 students
• C39 students
• D21 students
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The following table shows the frequency distribution of the heights of 100 students in a school:

 Height (cm) Total Number of Students 100 115– 120– 125– 130– 135– 140– 145– 12 12 20 16 12 10 18

How many students' heights are greater than or equal to cm?

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The following table shows the frequency distribution of the grades of 100 students in a science exam:

 Sets Total Frequency 100 0– 10– 20– 30– 40– 50– 6 15 12 26 23 18

How many students got 40 marks or more?

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The following table shows the frequency distribution of the grades of 100 students in an exam:

 Sets Total Frequency 100 0– 10– 20– 30– 40– 50– 5 25 21 16 19 14

Find the percentage of success given that the minimum grade for success is 20 marks.

• A
• B
• C
• D
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The following table shows the frequency distribution for the ages of 50 workers:

 Sets Total Frequency 50 20– 25– 30– 35– 40– 45– 50– 5 6 8 10 8 6 7

Draw the ascending cumulative frequency curve then determine the number of workers whose ages are less than 43.

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The following table shows the distribution of 1000 students’ scores in an exam:

 Scores Total Frequency 1000 20– 30– 40– 50– 60– 70– 80– 90– 123 127 127 131 129 127 133 103

Draw the ascending cumulative frequency curve, then determine the number of students whose scores are less than 85.

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The table below shows the scores of 73 students in an English exam. Find the value of .

 Scores Frequency 0– 5– 10– 15– 20– 25– 30– Total 6 5 6 15 11 12 73

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The years of experience of 100 workers in a factory ranges from 5 to 35 years. The table below shows the descending cumulative frequency distribution for the workers according to the years of experience. Fill in the frequency table below.

 Lower Boundaries of Sets Descending Cumulative Frequency 5 and more 10 and more 15 and more 20 and more 25 and more 30 and more 35 and more 100 89 77 61 42 28 0
 Years Frequency 5– 10– 15– 20– 25– 30– Total

• A100, 89,77, 61, 42, 28, 397
• B11, 28, 16, 19, 14, 28, 116
• C11, 12, 16, 19, 14, 28, 100
• D23,12, 16, 19, 14, 28, 112
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