Cumulative Frequency Analysis
A Grade 12 mathematics worksheet focusing on understanding, constructing, and interpreting cumulative frequency tables and graphs.
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Cumulative Frequency Analysis
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Read each question carefully and provide clear, detailed answers. Show all your work for calculations. Use the provided space for graphs and tables.
1. Cumulative frequency is the of frequencies for all values up to a certain point in a data set.
2. A cumulative frequency graph is also known as an .
3. The is the value that divides the data into two equal halves.
4. The following data shows the scores of 20 students in a math test:
55, 60, 62, 65, 68, 70, 70, 72, 75, 78, 80, 80, 82, 85, 88, 90, 92, 95, 98, 100
Construct a grouped frequency table and a cumulative frequency table for this data, using class intervals of width 10 (e.g., 51-60, 61-70, etc.).
5. A cumulative frequency graph for the heights of 50 plants is shown below. Use the graph to estimate the median height and the interquartile range (IQR).
6. Which of the following is NOT typically found on a cumulative frequency graph?
Median
Quartiles
Mode
Percentiles
7. If the total frequency is 80, what cumulative frequency corresponds to the upper quartile?
20
40
60
80
8. The table below shows the distribution of daily commute times (in minutes) for 100 employees at a company.
Commute Time (min) | Frequency
--------------------|-----------
0-10 | 15
11-20 | 25
21-30 | 35
31-40 | 18
41-50 | 7
a) Construct a cumulative frequency table for this data.
b) On the graph paper below, draw a cumulative frequency graph for the data.
c) Use your graph to estimate the number of employees who commute for less than 25 minutes.