# Working with Quantitative Data

## Why do we need to work with quantitative data?

Data are best used for a clearly identified purpose. The use of quantitative data is effective when we want to see how an individual or group is performing, identify any changes over time, or test to confirm a hunch or idea.

For example, it might be appropriate to calculate class averages to show the trend of student achievement over time.

## How to collect quantitative data?

Quantitative data can be collected from a variety of sources using different methods. This should be guided by the question or issue you are exploring. This ensures the data you collect are useful and targeted.

Common methods of collecting quantitative data in the school context include surveys, observations, student assessments, or school records.

For more rigorous learning on these, access the following AISNSW professional learning courses:

## How to analyse quantitative data

Quantitative data analysis involves reducing a set of numbers into a few statistics, or presenting them as graphs which are useful when interpreting the data.

Common forms of quantitative data analysis in the school context include the average, the median, and standard deviation.

## The mean (average)

The mean, or average is a common statistical measure used to summarise a dataset as a whole. It is calculated by adding up all the numbers in a dataset and dividing by how many numbers there are.

For example, when you want to see on average how many push-ups your students can do in a minute for a fitness test.

It is important to be aware that means are easily affected by extreme scores in a dataset. For this reason, we need to be careful when we use them. Read this article for more information about this.

## The median

The median is the middle score of a dataset when its scores are placed from lowest to highest. The median is particularly helpful when your dataset has extreme scores (high or low) which might skew the average. This is because the median is not affected by extreme scores.

## Standard deviation

Standard deviation (SD) is often reported with the mean to show the average spread of individual scores around the mean.

When SD is high, it means the individual scores are quite far from each other. When SD is low, it means the scores clump quite tightly together.

At times, datasets with the same means may have different SDs as their scores are distributed differently. Reporting SDs helps others understand how your data are distributed.

## Z-scores

Another useful statistical measure you might see in the school is z-scores, also called standard scores.

A z-score indicates how far above or below the mean an individual score is.

In a school context, z-scores may be used to determine a student’s position relative to the class average, measured in standard deviation units. Z-scores may also reveal whether a student has moved up or down in their learning progression in a subject over time.

The benefit of z-scores is that they allow scores from different tests to be compared on a common scale.

Consider the following simple example of a z-score graph:

- When a student’s z-score is 0 (on the 0 line), it means the student’s score is the same as the mean.
- When a student’s z-score is -1, it means the student’s score is 1 standard deviation
**below**the mean. - When a student’s z-score is 2, it means the student’s score is 2 standard deviation
**above**the mean.