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Grade 10 Mathematics Learners’ Book

INNODEMS

Subsection 3.1.2 Representing Data using a Frequency Distribution Table

Activity 3.1.3.

\(\textbf{Work in groups}\)
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  1. Below are the weekly pocket expenses (in Ksh) of a randomly selected group of \(25\) students.
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    \(120, 150, 180, 200, 220, 250, 270, 290, 300, 320, 350, 370, 390, 400,\)
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    \(420, 450, 470, 480, 490, 500, 340, 230, 280, 410, 330\)
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  2. Draw a grouped frequency distribution table with \(5\) classes to represent the data?
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  3. Identify the number with the highest frequency.
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  4. Compare your answer with others in class.
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Key Takeaway 3.1.11.

A frequency distrribution table is a table that shows an event and how many times it happens.
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There are two types:
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  • \(\textbf{Ungrouped Frequency Distribution}\text{:}\) for small datasets with individual values.
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  • \(\textbf{Grouped Frequency Distribution}\text{:}\) for large datasets where values are grouped into intervals.
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    \(\textbf{Steps to construct a grouped frequency distribution table}\)
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    1. Determine the Range of Data
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      \begin{align*} \textbf{Range} = \amp \textbf{ Maximum Value} - \textbf{ Minimum Value} \end{align*}
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    2. Decide the Number of Classes (Groups)
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    3. Calculate the Class Width
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      \begin{align*} \textbf{Class width} = \amp \frac{\textbf{ Range}}{\textbf{ Number of classes}} \end{align*}
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    4. Establish Class Boundaries
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      • Begin with the Lowest Value: Use the smallest data value as the lower limit of the first class.
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      • Determine the Upper Limit: Add the class width to establish the upper limit of the first class and the lower limit of the next class.
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      • Repeat the Process: Continue this pattern until all class intervals are created.
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    5. Tally the Frequencies
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      • Count how many data points fall within each class interval and record the frequency.
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    6. Complete the Table
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Example 3.1.12.

The following data represents test scores of \(20\) students in a grade \(10\) class.
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\(45, 50, 55, 50, 60, 70, 75, 80, 70, 55, 60, 65, 50, 55, 45, 60, 75, 80, 70, 50\)
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Prepare ungrouped frequency distribution table for the dataset.
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Solution.
Table 3.1.13.
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Test scores Tally Frequency
\(45\) \(//\) \(2\)
\(50\) \(////\) \(4\)
\(55\) \(///\) \(3\)
\(60\) \(////\) \(4\)
\(65\) \(/\) \(1\)
\(70\) \(///\) \(3\)
\(75\) \(//\) \(2\)
\(80\) \(//\) \(2\)
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Example 3.1.14.

The number of customers visiting a supermarket over \(30\) days were recorded as follows:
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\(135, 125, 140, 160, 145, 120, 150, 140, 130, 125, 135, 155, 140, 135, 130,\)
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\(155, 150, 160, 145, 140, 120, 145, 135, 140, 150, 130, 150, 125, 145, 120\)
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Draw a grouped frequency distribution table with \(5\) classes to represent the data?
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Solution.
To prepare frequency table for the grouped data above, we need to first find the range for the data.
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\begin{align*} \textbf{Range} = \amp \textbf{ Maximum Value} - \textbf{ Minimum Value} \end{align*}
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Maximum value = 160
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Minimum value = 120
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\begin{align*} \textbf{Range} = \amp 160 - 120\\ \amp 40 \end{align*}
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Range is \(40\)
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Next, Determine Class Width
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\begin{align*} \textbf{Class width} = \amp \frac{\textbf{ Range}}{\textbf{ Number of classes}}\\ \amp \frac{40}{5} = 8 \end{align*}
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Class widths are \(8\)
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Create Class Intervals
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Starting from 120, we create intervals of width 8:
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\(120 - 127\)
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\(128 - 135\)
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\(136 - 143\)
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\(144 - 151\)
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\(152 - 160\)
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Tally the Data
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We count how many values fall into each interval.
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\(120 - 127\text{:}\) \(120, 120, 125, 125, 125\)
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\(128 - 135\text{:}\) \(130, 130, 130, 135, 135, 135, 135\)
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\(136 - 143\text{:}\) \(140, 140, 140, 140, 140, 140\)
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\(144 - 151\text{:}\) \(145, 145, 145, 145, 150, 150, 150, 150\)
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\(152 - 160\text{:}\) \(155, 155, 160, 160\)
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Then construct the frequency Table
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Table 3.1.15.
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Test scores Tally Frequency
\(120 - 127\) \(\cancel{////}\) \(5\)
\(128 - 135\) \(\cancel {//////}\) \(7\)
\(136 - 143\) \(\cancel{/////}\) \(6\)
\(144 - 151\) \(\cancel{///////}\) \(8\)
\(152 - 160\) \(////\) \(4\)
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Exercises Exercises

1.

Twenty five students in Grade 10 recorded their time travel to school in minutes as follows:
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\(15, 8, 22, 30, 12, 25, 18, 10, 35, 20, 5, 28, 15, 40, 17, 23, 12, 32, 7, 19, 27, 14, 21, 9, 33\)
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Draw a frequency distribution table to represent the data.
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2.

Thirty customers at a service center recorded their wait times in minutes as follows:
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\(5, 12, 8, 15, 3, 10, 18, 6, 13, 9, 2, 16, 11, 7, 19, 14, 4, 8, 12, 20, 5, 17, 9, 13, 6, 11, 3, 15, 8, 14.\)
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Prepare a frequency distribution table for the set of data.
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3.

The costs (in Ksh.) of manufacturing equipment across different factories were recorded as follows:
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\(1250, 1425, 1580, 1720, 1850, 1975, 2100, 2235, 2370, 2480, 2610, 4310, 4425,\)
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\(2750, 2880, 3025, 3150, 3280, 3410, 3525, 3640, 3750, 3870, 3975, 4080, 4195,\)
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\(4550, 4680, 4820, 4950, 1380, 1625, 1890, 2340, 2570, 2780, 3120, 3390, 3610, \)
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\(4520, 4750, 3150, 2840, 1950, 2640, 3470, 4180, 3840, 4030, 4270.\)
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Prepare a frequency distribution table for the grouped data.
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4.

The annual rainfall (in mm) recorded in a region was as follows:
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\(625, 645, 670, 695, 720, 745, 770, 790, 810, 835, 860, 880, 905, \)
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\(1000, 1025, 1050, 1075, 1100, 1125, 1150, 930, 950, 975, 1180.\)
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Construct a grouped frequency distribution table for the data.
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Checkpoint 3.1.16.

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Checkpoint 3.1.17.

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