# Lesson Worksheet: Cumulative Frequency Graphs Mathematics

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.

 Mark Total Frequency 60 2– 6– 10– 14– 18– 22– 26– 11 10 13 7 6 5 8
• 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.

 Mark Total Frequency 60 2– 6– 10– 14– 18– 22– 26– 10 7 5 9 11 12 6
• 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.

 Mark Total Frequency 60 2– 6– 10– 14– 18– 22– 26– 12 10 9 10 6 11 2
• 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.

 Mark Total Frequency 60 2– 6– 10– 14– 18– 22– 26– 6 8 13 9 11 2 11
• 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.

 Mark Total Frequency 50 5–9 10–14 15–19 20–24 25–29 30– 5 10 9 10 12 4

Q6:

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

 Sets Total Frequency 50 300–399 400–499 500–599 600–699 700– 9 11 6 10 14

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) Total Number of Workers Number of Workers 100 15– 20– 25– 30– 35– 40– 23 14 12 15 19 17
• 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) Frequency 150≤ℎ≤155 155≤ℎ≤160 160≤ℎ≤165 165≤ℎ≤170 170≤ℎ≤175 4 22 56 32 5
• A165 cm
• B163 cm
• C160 cm
• D146 cm
• E155 cm

Q9:

Liam 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) Cumulative Frequency 15<𝑤≤20 15<𝑤≤25 15<𝑤≤30 15<𝑤≤35 15<𝑤≤40 15<𝑤≤45 2 6 15 36 58 73
• 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) Frequency 70≤𝑚≤80 80≤𝑚≤90 90≤𝑚≤100 100≤𝑚≤110 110≤𝑚≤120 4 12 34 32 26

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

Q13:

The table shows information about children who used the Internet last week.

 Hours (ℎ) Frequency 0≤ℎ<2 2≤ℎ<4 4≤ℎ<6 6≤ℎ<8 8≤ℎ<10 10≤ℎ<12 6 10 22 26 12 4

By drawing the cumulative frequency graph, find the number of children who used the Internet for less than 5 hours last week.

• A28 children
• B40 children
• C35 children
• D20 children
• E16 children

By drawing the cumulative frequency graph, estimate the median number of hours children used the Internet for to the nearest hour.

• A4 hours
• B7 hours
• C6 hours
• D5 hours
• E8 hours