Calculating Mean, Median, Mode and Range from a frequency Table (7)

Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data(ACMSP171)

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

Know:

  • How to add and divide numbers
  • How to order numbers from ascending/descending order
  • How to do a tally table

Understand:

  • That different types of data displays can be constructed to represent data.

Do:

  • I can calculate the mean for a set of data..
  • I can calculate the median for a set of data.
  • I can calculate the mode of a set of data.

Mean, Median, Mode and Range from a Frequency Table

Mean

To find the mean of a data set.

1) add all of the numbers
2) divide by the 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.

In this case, you have 1 score of 1, 1 score of 2, 3 scores of 3…

Mean = (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) / 30 (# of total items)

Mean = 6.2 (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 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” 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.

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 the data set is 9.

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