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examBoard: AQA
examType: GCSE
lessonTitle: Range as Measure of Dispersion
When psychologists collect data, they don't just want to know the average (mean) score - they also want to understand how spread out the scores are. This spread is called dispersion. The simplest way to measure dispersion is by calculating the range.
Key Definitions:
Imagine two classes took a psychology test and both got an average score of 60%. Does this mean both classes performed equally well? Not necessarily! In one class, everyone might have scored around 60%. In the other class, half the students might have scored 100% and half scored 20%. The average is the same, but the spread of scores is very different. Measuring dispersion helps us understand this difference.
Psychologists use several measures of dispersion:
In this lesson, we'll focus on the range.
The range is incredibly simple to calculate, which is why it's often the first measure of dispersion students learn:
Range = Highest value - Lowest value
Let's say a psychologist measured reaction times (in milliseconds) for 10 participants in a memory experiment:
320, 290, 350, 310, 400, 380, 330, 360, 420, 340
To find the range:
So the range of reaction times is 130 milliseconds.
A larger range indicates greater variability in the data. In our example, a range of 130 ms tells us that there's a considerable difference between the fastest and slowest reaction times. However, it doesn't tell us anything about how the other values are distributed between these extremes.
Psychologists use the range in various research contexts. Here are some examples:
In child development studies, researchers might record the age range at which children typically develop certain skills. For example, most children learn to walk between 9 and 15 months of age (range = 6 months).
When studying symptoms of mental health conditions, psychologists might report the range of scores on assessment scales. For example, on a depression scale from 0-63, a clinical sample might show scores ranging from 18 to 59 (range = 41).
In a famous study on short-term memory, participants were asked to recall a series of numbers. The researcher found that most people could remember between 5 and 9 items (range = 4), leading to the concept of "7 plus or minus 2" as the capacity of short-term memory. The range helped establish that there's natural variation in memory capacity among individuals.
One major limitation of the range is its sensitivity to outliers - extreme values that are much higher or lower than most of the data.
Consider these anxiety scores from 8 participants:
12, 15, 18, 14, 16, 17, 13, 85
Range = 85 - 12 = 73
The last score (85) is clearly an outlier. If we removed it:
Range = 18 - 12 = 6
The difference is dramatic! This shows how a single extreme value can make the range misleading.
Always look at your data before calculating the range. You can spot outliers by:
If you find outliers, consider whether they represent genuine data or possible errors.
When writing up psychological research, there are several ways to present the range:
While the range is useful, psychologists often need more sophisticated measures of dispersion:
Measures average distance from the mean. Takes all data points into account. Less affected by outliers than range. Most commonly used in research papers.
The range of the middle 50% of data. Ignores the highest and lowest 25%, making it resistant to outliers. Good for skewed distributions.
The average of squared differences from the mean. The standard deviation is its square root. Important in statistical tests but less intuitive to interpret.
A psychologist tested 10 students on their ability to recall words from a list. The scores (out of 20) were:
12, 15, 8, 14, 17, 13, 10, 16, 11, 9
Calculate the range:
Highest value = 17
Lowest value = 8
Range = 17 - 8 = 9
Interpretation: There is a difference of 9 points between the highest and lowest memory scores.
A researcher compared anxiety levels in two groups:
Group A: 15, 18, 22, 19, 16, 20 (Range = 22 - 15 = 7)
Group B: 8, 25, 12, 30, 15, 10 (Range = 30 - 8 = 22)
Interpretation: Group B shows much more variability in anxiety levels than Group A, even though both groups might have similar mean scores.
The range is the simplest measure of dispersion, calculated by subtracting the lowest value from the highest value in a dataset. While it's easy to calculate and understand, it's limited because it only uses two values and is heavily influenced by outliers. In psychological research, the range provides a quick overview of data spread but is often supplemented with more sophisticated measures like standard deviation.
Remember: When analyzing psychological data, looking at both central tendency (mean, median, mode) AND dispersion (range, standard deviation) gives you a more complete picture of your results!
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