Mathematics
Grade 10
15 min
Create frequency charts
Create frequency charts
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1
Introduction & Learning Objectives
Learning Objectives
Define key statistical terms including frequency, class interval, relative frequency, and cumulative frequency.
Organize a set of raw data into a frequency distribution table using appropriate class intervals.
Calculate the relative frequency and cumulative frequency for each class interval in a data set.
By the end of of this lesson, students will be able to construct a histogram to visually represent a frequency distribution.
Interpret a frequency chart to identify trends, patterns, and key features of a data set.
Determine an appropriate class width and number of classes for a given data set by analyzing its range.
Ever wonder how companies analyze thousands of customer reviews or how your teacher determines the grade distribution for a final exam? 📊...
2
Key Concepts & Vocabulary
TermDefinitionExample
Raw DataThe initial, unorganized collection of information or numbers gathered from a survey, experiment, or observation.The heights (in cm) of 10 students: 165, 172, 168, 175, 165, 180, 172, 171, 169, 175.
FrequencyThe number of times a specific value or an event occurs within a data set.In the data set {2, 3, 4, 3, 5, 3}, the frequency of the number 3 is 3.
Class Interval (or Bin)A range used to group data points. All intervals in a chart should have the same width.For test scores, a class interval could be 80-89, which includes all scores from 80 up to, but not including, 90.
Frequency Distribution TableA table that organizes data by listing the class intervals and the frequency (count) of data points that fall into each interval.A table showing intervals like 0-9...
3
Core Formulas
Class Width Calculation
Class Width ≈ (Maximum Value - Minimum Value) / (Desired Number of Classes)
Use this formula to determine a suitable width for your class intervals. First, find the range of your data (Max - Min). Then, decide on a reasonable number of classes (usually between 5 and 15). The result is an estimate; you should round it to a convenient number (like 5, 10, or 20).
Relative Frequency Formula
f_rel = f / n
To find the relative frequency (f_rel) of a class, divide its frequency (f) by the total number of data points (n). This gives you the proportion of the data in that class. Multiply by 100 to express it as a percentage.
Cumulative Frequency Calculation
F_i = Σ_{j=1 to i} f_j
The cumulative frequency (F) for a given class 'i' is the sum o...
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Challenging
A cumulative frequency table shows the following for the final three intervals: '30-39' has a cumulative frequency of 25, '40-49' has a cumulative frequency of 32, and '50-59' has a cumulative frequency of 35. What is the individual frequency of the '40-49' class interval?
A.32
B.7
C.3
D.57
Challenging
Given the trigonometry quiz data from Example 1 (Range: 19 to 48), a student proposes two different grouping schemes. Scheme A uses 3 classes (19-28, 29-38, 39-48). Scheme B uses the 5 classes from the tutorial (19-24, 25-30, etc.). Why is Scheme B a better choice for representing this data?
A.Scheme A has overlapping intervals.
B.Scheme B has a smaller total frequency.
C.Scheme A uses an incorrect class width formula.
D.Scheme A groups the data too broadly, hiding important details in the distribution.
Challenging
A student miscalculates cumulative frequency by adding the current frequency to the *total* number of data points instead of the previous cumulative frequency. Using the frequencies from Example 1 (2, 4, 5, 6, 3) and a total of 20, what value would appear in the final row of their incorrect cumulative frequency column?
A.20
B.17
C.23
D.3
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