Worksheet: Cumulative Frequency Graphs

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In this worksheet, we will practice drawing a cumulative frequency diagram and using it to make estimations about the data.

Q1:

The table shows the marks of 60 students in a mathematics exam. By drawing a cumulative frequency curve, estimate the median mark achieved.

Mark2–6–10–14–18–22–26–Total
Frequency1110137658 60
  • A21
  • B6.8
  • C6.5
  • D34
  • E12.8

Q2:

The table shows the marks of 60 students in a mathematics exam. By drawing a cumulative frequency curve, estimate the median mark achieved.

Mark2–6–10–14–18–22–26–Total
Frequency1075911126 60
  • A22
  • B9.5
  • C10
  • D31
  • E17.6

Q3:

The table shows the marks of 60 students in a mathematics exam. By drawing a cumulative frequency curve, estimate the median mark achieved.

Mark2–6–10–14–18–22–26–Total
Frequency12109106112 60
  • A22
  • B9
  • C8
  • D31
  • E13.6

Q4:

The table shows the marks of 60 students in a mathematics exam. By drawing a cumulative frequency curve, estimate the median mark achieved.

Mark2–6–10–14–18–22–26–Total
Frequency6813911211 60
  • A27
  • B9.5
  • C10
  • D36
  • E15.3

Q5:

The table shows the distribution of marks students attained in a mathematics exam. By drawing a cumulative frequency curve, estimate the median mark attained.

Mark5–910–1415–1920–2425–2930–Total
Frequency51091012450

Q6:

By drawing a cumulative frequency curve, find the median of the following frequency distribution.

Sets300–399400–499500–599600–699700–Total
Frequency9116101450

Q7:

The table shows the distribution of daily wages of 100 workers at a factory. By drawing a cumulative frequency curve, estimate the median daily wage.

Daily Wages (LE)15– 20– 25– 30– 35– 40– Total Number of Workers
Number of Workers231412151917100
  • A35 LE
  • B30 LE
  • C64 LE
  • D49 LE

Q8:

The following data represents the height of some students in a high school. Use the cumulative frequency graph to estimate the median.

Height (cm)150≤ℎ≤155155≤ℎ≤160160≤ℎ≤165165≤ℎ≤170170≤ℎ≤175
Frequency42256325
  • A165 cm
  • B163 cm
  • C160 cm
  • D146 cm
  • E155 cm

Q9:

Ethan took a sample of 100 balls from box A. He weighed each ball and recorded its weight. He used the information to draw the cumulative frequency graph shown on the grid. Use the cumulative frequency graph to find an estimate for the median weight of the balls.

  • A50 grams
  • B80 grams
  • C104 grams
  • D120 grams
  • E90 grams

Q10:

By drawing a cumulative frequency graph for the given data that shows the weights of different students, determine which of the following could be an estimate for the median weight from the graph?

Weight, 𝑤 (kg)15<𝑤≤2015<𝑤≤2515<𝑤≤3015<𝑤≤3515<𝑤≤4015<𝑤≤45
Cumulative Frequency2615365873
  • A38 kg
  • B35 kg
  • C30 kg
  • D39 kg
  • E32 kg

Q11:

If a cumulative frequency diagram were drawn from the data given in the table, what would be the highest cumulative frequency?

Time, 𝑚 (Minutes)70≤𝑚≤8080≤𝑚≤9090≤𝑚≤100100≤𝑚≤110110≤𝑚≤120
Frequency412343226

Q12:

From the following cumulative frequency graph that represents the masses of some balls that have different colors, find the median.

  • A2.7 kg
  • B2.1 kg
  • C2.9 kg
  • D1.7 kg
  • E3.1 kg

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