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Frequency & Frequency Tables

Frequency is the number of times a partciaular value of data occurs.
For example: say we ask \(10\) people which color they prefer between blue, red and green. The answers we get are:

blue, green, green, red, blue, blue, blue, red, blue, red
Then the frequency of each of the colors is:
  • frequency of blue: \(5\)
  • frequency of green: \(2\)
  • frequency of red: \(3\)
To summarize the frequence of each value of data, we usually use frequency tables.

The objective of this section is to know how to construct frequency tables for both:

  • Qualitative Data
  • Discrete Quantitative Data.
The method is the same for both of these data types.

Note: if you're unsure what these two types of data are, make sure to read through the previous section in which we define the different types of data.

We start by watching a tutorial to learn the method. We then work through some exercises.

Method

  • Step 1: Contruct a table with \(3\) columns named:
    • Observations
    • Tally
    • Frequency
    and always and space for the total sum of all the frequencies, below the frequency column.
  • Step 2: Complete the tally column by adding a "tick" in the appropriate row each time you come across a new data value.
  • Step 3: Complete the frequency column by counting the total number of ticks you see on each row; the frequency of each data value equals to the total number of ticks you see for that data value.
This three-step method will make more sense in the following example.

Example

In a survey \(50\) people were asked which color t-shirt they prefer, Red, Blue, Green, Yellow, Orange, Pink, Black or White.

The raw data (before any organizing is done) is shown here:

blue, blue, blue, red, green, green, pink, black, black, white, white, yellow, white, black, white, black, pink, green, red, white, red, black, black, black, orange, white, black, blue, pink, blue, blue, green, yellow, black, yellow, red, orange, red, red, yellow, pink, blue, white, orange, black, red, blue, white, green, red

To construct a frequency table for this data we follow our three-step method:

  • Step 1: Contruct a table with \(3\) columns named:
    • Observations
    • Tally
    • Frequency
    That would look something like this:
  • Step 2: Complete the tally column by adding a "tick" in the appropriate row each time you come across a new data value.
    That would look something like this:
  • Step 3: Complete the frequency column by counting the total number of ticks you see on each row; the frequency of each data value equals to the total number of ticks you see for that data value.
    That would look something like this:
    Notice that the total sum of all the frequencies equals to the number of people we surveyed, \(50\), which is exactly what it should do.

Tutorial

Exercise

  1. A sports club orders \(30\) jerseys for its students. The possible sizes are:
    Extra Small (XS), Small (S), Medium (M), Large (L), Extra Large (XL).
    After asking each student to write their size on a sheet of paper the club owner is faced with the following raw data:

    S, XS, L, M, XL, M, M, M, S, L, L, XS, XL, M, XL, S, XS, L, M, M, S, L, M, M, M, S, S, L, XS, L

    Using a tally chart, summarize this data in a frequency table.
  2. \(30\) students sat the same mathematics test, which was graded out of \(10\). The grades obtained are shown here:

    9, 10, 9, 9, 8, 5, 6, 4, 4, 7, 6, 2, 10, 5, 8, 9, 7, 6, 7, 8, 5, 4, 1, 9, 9, 8, 6, 7, 10, 1.
    Construct a frequency table to summarize these results.

  3. A mini golf owner wishes to better target his weekend customers. To do that he starts by observing the age group of the customers entering the gold on a Saturday.
    Each time a customer enters the mini golf he makes a note of whether they are:
    child (C), teenager (T), young adult (Y), middle-aged (M), senior (S)
    By the end of Saturday morning, the raw data the owner collected was:
    Y, C, C, T, S, T, T, M, Y, Y, M, C, C, C, T, S, M, Y, T, S, Y, T, S, T, Y, C, T, T, M, T, C, T, S, C, C, Y
    1. Construct a frequency table for this data.
    2. How many people went visited the mini golf that Saturday morning?
  4. The number of goals scored in each game of a football (soccer) tournament are listed, below, in the order in which the games took place:
    5, 3, 1, 5, 0, 2, 4, 1, 2, 4, 0, 4, 4, 1, 0, 3, 1, 4, 2, 1, 4, 3, 1, 1, 3, 5, 1, 2, 2, 4

Answers Without Working