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The number of times a particular data value occurs is known as the frequency. A frequency table is used to organise data and determine the number of times a particular data value occurs.

Mathematics

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Step-by-step solution

4 steps
  1. List all the marks from the table.

    The marks obtained in the Grade 8 Mathematics test are:
    33, 23, 38, 34, 90, 51, 80, 87, 43, 37
    58, 65, 17, 45, 70, 53, 91, 23, 37, 96
    89, 15, 17, 64, 96, 1, 57, 6, 13, 74
    80, 98, 63, 88, 81, 78, 81, 88, 93, 68
    There are a total of 40 marks.

  2. Determine appropriate class intervals for the marks.

    The lowest mark is 1 and the highest mark is 98. We will use class intervals of 10, starting from 0.
    The intervals are: 0−90-9, 10−1910-19, 20−2920-29, 30−3930-39, 40−4940-49, 50−5950-59, 60−6960-69, 70−7970-79, 80−8980-89, 90−9990-99.

  3. Tally the marks into their respective intervals and count the frequency.

    • 0−90-9: 1, 6 (2 marks)
    • 10−1910-19: 17, 15, 17, 13 (4 marks)
    • 20−2920-29: 23, 23 (2 marks)
    • 30−3930-39: 33, 38, 34, 37, 37 (5 marks)
    • 40−4940-49: 43, 45 (2 marks)
    • 50−5950-59: 51, 53, 57, 58 (4 marks)
    • 60−6960-69: 65, 64, 63, 68 (4 marks)
    • 70−7970-79: 70, 74, 78 (3 marks)
    • 80−8980-89: 80, 87, 89, 80, 81, 88, 81, 88 (8 marks)
    • 90−9990-99: 90, 91, 96, 96, 98, 93 (6 marks)
  4. Construct the tally and frequency table.

    Mark (m)TallyFrequency0−9||210−19||||420−29||230−39||||| 540−49||250−59||||460−69||||470−79|||380−89||||| |||890−99||||| |6\begin{array}{|c|c|c|} \hline \textbf{Mark (m)} & \textbf{Tally} & \textbf{Frequency} \\ \hline 0-9 & \text{||} & 2 \\ 10-19 & \text{||||} & 4 \\ 20-29 & \text{||} & 2 \\ 30-39 & \text{||||| } & 5 \\ 40-49 & \text{||} & 2 \\ 50-59 & \text{||||} & 4 \\ 60-69 & \text{||||} & 4 \\ 70-79 & \text{|||} & 3 \\ 80-89 & \text{||||| |||} & 8 \\ 90-99 & \text{||||| |} & 6 \\ \hline \end{array}

    The final answer is The tally and frequency table for the marks is shown above.\boxed{\text{The tally and frequency table for the marks is shown above.}}.
    What's next?

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