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6.01 Frequency data displays

Lesson

Frequency data displays are a visual way of presenting information to highlight the frequency (count) of each response or a group of responses. They can be really useful as they help us sort and order the information we collect and present it in a clear, concise way. Selecting a good type of data display is really important and the best type will depend on the type of information you need to display.

Frequency Tables

In Data in a table, we learned that instead of writing a data set in a long list, it is often better organize it in a table when collecting it. One common way to keep track of data is to create a frequency table and keep a tally of the results. Frequency tables can be used for categorical (qualitative) or numerical (quantitative) data.

Frequency refers to how often an event occurs. We often construct frequency tables as an easy way to keep track of and display data because we can have:

  • One column as a list showing the possible outcomes that may occur
  • A second column with tally marks of the frequency of each event (although this column isn't always included), and
  • A third with the total frequency as a number.  
Example
Color of Car Tally Frequency
Black |||| ||| $8$8
White |||| |||| $9$9
Blue |||| || $7$7
Green |||| $4$4

Grouped frequency tables

In Chunks of data, we learned that if numerical data is continuous or discrete and very spread out, then we can make each row of a frequency table a group of values, instead of just a single value. We call the groups of values classes or intervals.

Example: This grouped frequency table shows the cost per gallon at 15 different gas stations across the USA.

Price (in cents per gallon) Frequency
$200.0$200.0-$224.9$224.9 $8$8
$225.0$225.0-$249.9$249.9 $4$4
$250.0$250.0-$274.9$274.9 $2$2
$275.0$275.0-$299.9$299.9 $1$1

Dot plots

In Going dotty, we learned that dot plots can be used for both categorical or numerical data. The horizontal axis will have the responses listed and then the number of dots show the frequency of that response.

We start off with a kind of number line or a list of all the possible outcomes in our study. For example, if the number of children in peoples' families ranged between $1$1 and $5$5, I would construct my dot plot with all the possible values we could have scored: $1,2,3,4$1,2,3,4 or $5$5:

Each of these possible values is written on a number line. The number of dots above each score corresponds to the frequency of each score. For example, in the dot plot above, we can see that 3 families have one child, 8 families have two children and so on.

Histograms and column graphs

Histograms are similar to bar or column graphs. There are 2 main differences:

  1. Bar or column graphs are usually used to display categorical data, whereas histograms are used to display only numerical data 

  2. Bar and column graphs are drawn with spaces between the columns whereas histograms do not have spaces between the columns.

Histograms can display discrete or continuous numerical data, but are most often used for continuous data.

Example 1: categorical data - COLUMN GRAPH

Each student in a class was surveyed and asked the color of their eyes.   The data is categorical and the results are displayed in a column graph below:

Example 2: Numerical and discrete - histogram

The data that was collected in the survey below is called discrete data because it can only take particular values (in this case whole numbers).  In histograms that display discrete data the mark is located in the center of the columns.  The height of each column represents the frequency of each data item.

Each student in a class was surveyed and asked the size of their families.   The data is numerical and the results are displayed in a histogram below:

 

Example 3 - numerical and continuous - Histogram

The data that was collected in the survey  is called continuous data because it can take any value within a range.  In histograms that display continuous data the column width represents the range of each interval or bin. The height of each column represents the frequency of each data item within each interval.

Each student in a class was surveyed and asked their heights.   The data is numerical and the results are displayed in a histogram below:

 

Worked Examples

Question 1

Christa is a casual nurse. She used a dot plot to keep track of the number of shifts she did each week for a number of weeks.

  1. Over how many weeks did Christa record her shifts?

  2. For how many weeks did she work $5$5 shifts?

    $\editable{}$ weeks

  3. How many weeks did she work less than $6$6 shifts?

    $\editable{}$ weeks

  4. When Christa works at least $6$6 shifts a week, she buys a weekly train ticket. What proportion of the time did she buy a weekly train ticket?

QUESTION 2

Consider the histogram below, showing the length of a number of phone calls.

Phone CallsLength of call (in minutes)Number of calls510151234567

  1. Complete the frequency table.

    Length of call (to the nearest minute) Number of calls
    $1$1 $\editable{}$
    $2$2 $\editable{}$
    $3$3 $\editable{}$
    $4$4 $\editable{}$
    $5$5 $\editable{}$
    $6$6 $\editable{}$
    $7$7 $\editable{}$
  2. What is the total number of minutes spent on phone calls?

  3. If you receive $123$123 minutes of free calls, and are charged $\$1.00$$1.00 per minute afterwards, what is your total spending?

    Give your answer correct to two decimal places.

QUESTION 3

The following table shows the number of trains arriving either on time or late at a particular station.

Day Number of trains arriving on time Number of trains arriving late
Monday $23$23 $28$28
Tuesday $12$12 $25$25
Wednesday $22$22 $29$29
Thursday $30$30 $27$27
Friday $11$11 $14$14
Saturday $15$15 $11$11
Sunday $14$14 $10$10
  1. How many trains were late on Friday?

  2. How many trains passed through the station on Wednesday?

  3. How many trains were on time throughout the entire week?

  4. What proportion of trains were on time over the whole week?

    Leave your answer as a fraction.

QUESTION 4

Construct a histogram to represent the following data:

$46,47,48,48,48,47,50,47,48,50,47,46,49,49,50,49,48,47,46,50,48,51,51,50,50,47,49,48,51,49,50,51$46,47,48,48,48,47,50,47,48,50,47,46,49,49,50,49,48,47,46,50,48,51,51,50,50,47,49,48,51,49,50,51

  1. HistogramScoresFrequency510464748495051

QUESTION 5

In product testing, the number of faults detected in producing a certain machinery is recorded each day for several days. The frequency table shows the results.

Number of faults Frequency
$0-3$03 $10$10
$4-7$47 $14$14
$8-11$811 $20$20
$12-15$1215 $16$16
  1. Construct a histogram to represent the data.

    Faulty MachineryNumber of FaultsFrequency10201.55.59.513.5

  2. What is the least possible number of faults that could have been recorded on any particular day?

    $\editable{}$ faults

Outcomes

S-ID.1

Represent data with plots on the real number line (dot plots, histograms, and box plots).

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