_{Up Learn – A Level maths (edexcel) – Measures of Spread – The Interquartile Range}

_{Up Learn – A Level maths (edexcel) – Measures of Spread – The Interquartile Range}

**How to Work out Interquartile Range: Summary**

**Here’s a summary of everything you need to know about the interquartile range for A Level, including how to work out the interquartile range.**

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### More videos on Measures of Spread – The Interquartile Range:

^{The Problem with Range (free trial)}

^{Quartiles (free trial)}

^{The Interquartile Range (free trial)}

^{How do we cut data into quarters? (free trial)}

^{Finding the Position of Quartiles (free trial)}

^{Rounding the Position of Quartiles (Article) (free trial)}

^{The Values of Quartiles Between Data Points (free trial)}

^{Finding Quartiles from Frequency Tables (free trial)}

^{Finding Quartiles of Continuous Data (free trial)}

## Univariate Data

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2. Quantitative and Qualitative Variables

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3. Continuous and Discrete Variables

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4. What are Data?

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5. Types of Data

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6. Introduction

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7. Frequency Tables

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8. Frequency Tables and Quantitative Data

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9. Grouped Frequency Tables

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10. Parts of the Grouped Frequency Table

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11. Hidden Boundaries

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12. Finding Class Boundaries

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13. Grouped Frequency Tables with Boundaries

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14. Class Widths and Midpoints

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2. Linear Interpolation

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3. Linear Interpolation and Tables

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4. Reading Grouped Frequency Tables

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5. Cumulative Frequency Counts

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6. Interpolating Frequency Counts in Subclasses

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7. Interpolating Frequency Counts- Shortcuts

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2. The Modal Class Interval

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3. More Measures of Central Location

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4. The Total Number of Data Points

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5. Sigma Notation

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6. Central Location – Mean

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7. Sigma Notation Part 2

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8. Calculating a Mean from Frequency Tables

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9. Estimating a Mean from Grouped Frequency Tables

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10. Central Location – Median

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11. Describing the Location of the Median

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12. Finding the Median in a Large Data Set

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13. Central Tendency and Symmetric Distributions

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14. Positively and Negatively Skewed Distributions

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2. Quartiles

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3. The Interquartile Range

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4. How do we cut data into quarters?

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5. Finding the Position of Quartiles

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6. Rounding the Position of Quartiles (Article)

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7. The Values of Quartiles Between Data Points

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8. Finding Quartiles from Frequency Tables

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9. Finding Quartiles of Continuous Data

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10. Another Measure of Location

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11. Percentiles

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12. Percentiles and Quartiles

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13. Finding the Position of Percentiles

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14. Spread – The Interpercentile Range

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15. What’s So Great About Interpercentile Ranges?

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2. Dealing with Outliers

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3. Strategy 1: Finding Outliers Using Quartiles (Part 1)

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4. Strategy 1: Finding Outliers Using Quartiles (Part 2)

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5. Strategy 1: The Constant k

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6. Another Strategy for Finding Outliers

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7. Deviation

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8. Finding the Average Deviance

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9. Step 1: Sxx

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10. Step 2: Variance

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11. Step 3: Standard Deviation

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12. Strategy 2: Finding Outliers Using Standard Deviation

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13. Mean Absolute Deviation

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14. Removing Anomalies

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15. SD and Variance: Measures of Spread

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16. Finding Variance/SD: A Shortcut Part 1

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17. Finding Variance/SD: A Shortcut Part 2

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18. Finding the Variance/SD from a Frequency Table

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19. Finding the Variance/SD from a Grouped Frequency Table

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20. Comparing Data Sets

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2. Coding Data

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3. Rules for Coding Data

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4. Rules Involving Subtraction

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5. Rules Involving Subtraction and Division

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6. Decoding Data

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7. Finding the Mean of Coded Data

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8. Finding the Standard Deviation of Coded Data

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9. How Mean and Standard Deviation are Affected by Coding

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2. Box Plots

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3. Box Plots with Outliers

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4. Comparing Box Plots

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5. Another Way to Estimate Data

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6. Plotting Cumulative Frequency Diagrams

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7. Reading Cumulative Frequency Diagrams

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2. Why is a Histogram Not a Bar Chart? – Part 1

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3. Why is a Histogram Not a Bar Chart? – Part 2

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4. Why Do Histograms Use Area to Represent Frequency?

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5. Plotting A Histogram – Part 1

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6. Plotting A Histogram – Part 2

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7. Histogram Questions – Part 1

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8. Histogram Questions – Part 2

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9. Frequency Polygons

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2. What is a Population?

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3. What is a Census?

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4. Censuses: Pros and Cons

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5. Samples and Inferences

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6. Why is it Called a Sampling Frame?

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7. Samples Should Be Representative

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8. Sample Size

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9. Types of Sampling

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10. Opportunity Sampling

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11. Opportunity Sampling: Pros and Cons

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12. Quota Sampling

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13. Quota Sampling: Pros and Cons

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14. Random Sampling vs Non-Random Sampling

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15. Simple Random Sampling

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16. Simple Random Sampling: Pros and Cons

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17. Systematic Sampling

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18. Systematic Sampling: Pros and Cons

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19. Stratified Sampling

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20. Stratified Sampling: Pros and Cons

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Here’s a reminder of the key points you should know about the interquartile range.

There are a few different types of measure of spread.

One of those is the range, which we find if we take the largest value in a dataset and subtract the smallest value.

However, if the dataset has extreme values, the range can be misleading.

So to avoid this problem, we can turn to measures of location, called quartiles.

The middlemost value of a data set is called the second quartile.

The value that’s a quarter of the way through is called the first quartile.

And the value that’s three quarters of the way through is called the third quartile.

And we can represent quartiles like this.

These enable us to create a new measure of spread, called the interquartile range [fit in knowledge structure]

…Which is the distance the first quartile and the third quartile.

And it spans the middle fifty percent of a data set.

Now, splitting datasets into quarters is harder than it might first appear and depends on the number of data points.

As a result, you’ll find different people use different methods, and they can be a bit messy.

We recommend using this formula to find the position of any quartile.

Where q represents the number of the quartile, and n represents the total number of data points.

Now, the position of a quartile must always be a multiple of 0.5.

But occasionally, …

using this formula might get you a result like this or this

If you’re looking for a first quartile and get one of these, always round up to the nearest point five.

And if you’re looking for a third quartile and get one of these, always round down to the nearest point five.

We can also find the value of a quartile.

If the quartile’s position is halfway between two data points, its value is given by the average of the data points on either side.

Finally, when the data set is shown in a frequency table, we can find the value of a quartile by first finding its position.

Then, the cumulative frequency counts.

And lastly, locating the value of a data point at that position.

And when the dataset is shown in a grouped frequency table, we can estimate the value of a quartile using linear interpolation.

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