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The final part of the research unit is descriptive statistics. Researchers would typically use descriptive statistics during stage 6 of the research process (examine data).
You will be expected to calculate some descriptive statistics using a simple dataset so this is stuff you need to know!
why though?!
why though?!
After a researcher has collected their data, they need to examine that data to turn it into meaningful results which can be compared, interpreted, communicated with stakeholders, etc... This is where descriptive statistics come in.
Descriptive statistics "are brief descriptive coefficients that summarize a given data set, which can be either a representation of the entire or a sample of a population. Descriptive statistics are broken down into measures of central tendency and measures of variability (spread)"
Look at this image - what 'makes more sense' to our human brains at-a-glance?
What would happen to the complexity of the raw data versus the charts and tables if another 100000 respondents took part?
At level 5, we need to be able to apply some descriptive statistics to a simple dataset. We're focussing on the 'measures of central tendency'.
USE THESE THREE AS PAGE / SECTION HEADINGS IN YOUR NOTES
USE THESE THREE AS PAGE / SECTION HEADINGS IN YOUR NOTES
MEAN - MEDIAN - MODE
MEAN - MEDIAN - MODE
THE MEAN (AKA THE AVERAGE)
THE MEAN (AKA THE AVERAGE)
The mean is one of the most useful descriptive statistics we can calculate to get an at-a-glance understanding of our data, particularly if you're comparing two different groups (for example, scores at darts before and after 15 shots of vodka).
You use means ALL THE TIME without thinking about. If someone asks you how long it takes to drive / walk from A to B, you don't reel off a list of every single time you've made that journey and how long it took, you'll just say "about 15 minutes"...
calculating the mean
calculating the mean
THE MEdian (aka the middle number)
THE MEdian (aka the middle number)
If you coped with the mean, the median and mode should be a piece of cake. Sometimes it's useful to know where the 'middle' of our values is too. To do this we simply calculate the median...
To work out the MEDIAN we simply list all the numbers in order (smallest to biggest or biggest to smallest, it doesn't matter) and find the one that is in the MIDDLE
Imagine you've been given the task of deciding what age-appropriate entertainment to put on for a party where there will be some children present... You calculate some descriptive statistics on the ages to see what's what...
Psst! When you have a dataset with an even number of samples you will find 2 'middle' numbers... all we need to do in these instances is take the mean of these 2 numbers (by adding them together and dividing by 2).
THE Mode (aka the number that appears the most)
THE Mode (aka the number that appears the most)
The mode is simply the value that occurs most often within your dataset. Similar to the median, it's handy to put your data into order at this point as it makes it easier to work out. Continuing with the example above...
WHAT IF SOME NUMBERS APPEAR THE SAME AMOUNT OF TIMES?
WHAT IF SOME NUMBERS APPEAR THE SAME AMOUNT OF TIMES?
Your turn...
Your turn...
If you think you're ready, give the examples on this website a try. Keep a track of any mistakes you make and see if you can work out where you went wrong (we only learn from our mistakes if we acknowledge them)
In summary...
activities
activities
Please submit your responses to this activity to Research Methods Five - Descriptive Statistics on G classroom
You've been recruited by a residential care facility. One of your first jobs is to determine some age-appropriate activities for the residents. You're given a dataset containing the ages of the residents.
Calculate the mean, median and mode for the dataset and suggest an age-appropriate activity for the group
Show your working (no marks without it!)
Think-about-it-question: Why might measures of central tendency not be the best kind of statistics to use here?
Resident ages: 56, 41, 21, 47, 89, 63, 92, 42, 32, 58, 64, 65, 76, 46, 34, 39, 95, 84, 64
2. Impressed by your mathematical wizardry, your boss asks you to do some further analysis for them. They've been trying out the residents on different diets - half the residents (we'll call them group 1) have had a low sugar, low caffeine diet while the other half (group 2) have been trialling a high sugar, high caffeine diet. Your boss is concerned about how the differences in diet might be affecting residents' sleep so asks staff to record the number of hours slept (rounded to the nearest hour) for each group.
Use your knowledge of descriptive statistics to work our the measures of central tendency for each group.
Which diet would you recommend? WHY? <- this is important, don't skip it. Working out results is pointless unless we understand what they mean for real life (i.e., a conclusion!)
Group 1 Sleep Hours
7, 8, 7, 8, 6, 7, 7, 6, 9, 8, 7, 6, 5, 7, 9, 8,10
Group 2 Sleep Hours
7, 8, 7, 6, 5, 6, 7, 8, 6, 6, 9, 5, 7, 6, 8, 9, 6
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