Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data (VCMSP270)

LO: To calculate the mean, median, mode and range for a set of data from a frequency table.

Know:

  • How to add, multiply and divide numbers.

  • How to order numbers from ascending/descending order.

  • How to create a tally table and interpret the results from a tally table.

Understand:

  • that summarising data by calculating measures of centre and spread can help make sense of the data.

Do:

  • I can calculate the mean for a set of data from a frequency table.

  • I can calculate the median for a set of data from a frequency table.

  • I can calculate the mode of a set of data from a frequency table.

Calculating the Mean, Median, Mode and Range from a Frequency Table

Sometimes when we collect data, it’s not the most productive when the data is not organised and spread out all over the place.

Imagine having to read the list of results as, 7, 1, 3, 8, 5, 6, 7, 8, 9, 10, 3, 5, 6, 7, 8, 8, 5, 6, 6, 7, 3, 6, 9, 7, 8, 2, 4, 5, 7, 7, 9.

It would be very hard work trying to keep track of which numbers you counted and which you haven’t.

One quick way to organise data collected is the use of a frequency table (tally table). This methodology helps us to arrange the collected data into a much easier to interpret way.

Mean

To find the mean of a data set.

1) add all of the numbers to find the sum of the whole data set.
2) then divide by the total number of items in the data set.

It is a little bit different if you have to find the mean when given a frequency table.

You have to first calculate the total score of everything, but the frequency table helps us to quickly calculate the total sum.

In this case, you have 1 score of 1, 1 score of 2, 3 scores of 3, so all I have to do is multiply the value of each row by the freqency.

Since I have 1 value of 1 I know that line would have a value of 1, I have 1 score of 2 so that line would have a value of 2, I also have 3 scores of 3 which gives a value of that line of 9.

Total Value = (1 x 1) + (2 x 1) + (3 x 3) + (4 x 1) + (5 x 4) + (6 x 5) + (7 x 6) + (8 x 5) + (9 x 3) + (10 x 1) = 185

Total Number of items = 30

Mean = 185 / 30

Mean = 6.17 (rounded to 2 decimal places)

Median

Median is also known as the middle. The median shows you what the middle number is that splits the data in half so that half the data is on one side and the other half is on the other.

To find the median of a data set.

1) arrange the numbers in order (ascending/descending doesn’t really matter)
2) find the middle number
3) if there are 2 middle numbers, you will have to find the middle between the two numbers.

Since the data is already in ascending (lowest to highest) order, all we need to do is find the middle number. We have 30 total items. Since it is an even number, we need to find the average (mean) of the 15th and 16th numbers.

The 15th number would be 6 and the 16th number would be 7, so the average of 6 and 7 would be 6.5.

So the median of this data set would be 6.5.

Mode

Mode is also known as the “most popular/common” number/item.
In this data set it would be the most tallied number, which is 7 as it has 6 tallies.

Range

Range is the difference between the lowest (minimum) and highest (maximum) values. It determines how spread out the data set is.

In this data set the range would be the highest value subtract the lowest value.

The highest (maximum value) is 10, the lowest (minimum value) is 1. So the range of this data set is 9.

Videos on Calculating the Measures of Centrality Using Frequency Tables

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