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Secondary

Create and interpret dot plots II

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Lesson

Dot plots are a graphical way of displaying the frequencies of discrete quantitative or categorical data. In other words, they show how often a particular choice was made or how many times an event occurred. They are best used for small to medium size sets of data and are good for visually highlighting how the data is spread and whether there are any outliers that may change our measures of central tendency, particularly the mean and the median.

 

How to construct or read a dot plot

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.

Now let's look at some dotty examples!

Worked Examples

Question 1

The goals scored by a football team in their matches are represented in the following dot plot.

  1. Complete the following frequency distribution table.

    Goals scored Frequency
    $0$0 $\editable{}$
    $1$1 $\editable{}$
    $2$2 $\editable{}$
    $3$3 $\editable{}$
    $4$4 $\editable{}$
    $5$5 $\editable{}$

QUESTION 2

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.

A dot plot has its horizontal axis labeled "Shifts per Week" and marked at intervals of 1, ranging from 3 to 8. Above each number of shifts on the horizontal axis, a vertical stack of red dots represent the number of weeks. At 3 shifts, 1 red dots are stacked. At 4 shifts, 5 red dots are stacked. At 5 shifts, 4 red dots are stacked. At 6 shifts, 7 red dots are stacked. At 7 shifts, 2 red dots are stacked. At 8 shifts, 2 red dots are stacked.

  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 3

The number of 'three-pointers' scored by a basketball team in each game of the season is represented in the dot plot. A 'three-pointer' is worth 3 points.

  1. What was the total number of points scored from three-pointers during the season?

  2. What was the average number of points scored from three pointers each game of the season? Round to two decimal places if necessary.

 

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