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Number of Observations


The number of scores in a data set is also called the total frequency. The number of scores in a data set is simply how many numbers there are written down. For example, if you survey $40$40 people, then you will have $40$40 scores in your data set.

To find the number of scores in a set, we simply have to count all the scores in our set. For example, if we had the numbers $17$17, $19$19 and $22$22 in a data set, we could count the scores and say that the number of scores (or the total frequency) is $3$3 because there are three numbers in the set.

Worked Examples

Question 1

Ms Barnett has just marked a set of homework. The scores she gave were:


  1. How many pieces of homework did Ms Barnett mark?



Aaron has been recording the number of goals he has scored in soccer matches so far this year.


  1. How many soccer games has Aaron played so far this year?

  2. What is the total number of goals Aaron scored in all matches?


A teacher has marked a set of tests and put the scores of her class into the table below.

Score Frequency
$26$26 $13$13
$27$27 $8$8
$28$28 $2$2
$29$29 $19$19
$30$30 $5$5
  1. How many students took the test?


The frequency polygon below shows the scores awarded to a mathletes team during several recent competitions.

Frequency PolygonScoresFrequency102028293031323334

  1. How many competitions have the mathletes team taken part in recently?




Plan and conduct surveys and experiments using the statistical enquiry cycle:– determining appropriate variables and measures;– considering sources of variation;– gathering and cleaning data;– using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets;– comparing sample distributions visually, using measures of centre, spread, and proportion;– presenting a report of findings

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