_{Up Learn – A Level maths (edexcel) – Outliers and Standard Deviation}

_{Up Learn – A Level maths (edexcel) – Outliers and Standard Deviation}

**Outliers and Standard Deviation Summary**

**Here’s a summary of everything you need to know about outliers and standard deviation for A Level.**

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### More videos on Outliers and Standard Deviation:

^{Introduction: Outliers (free trial)}

^{Dealing with Outliers (free trial)}

^{Strategy 1: Finding Outliers Using Quartiles (Part 1) (free trial)}

^{Strategy 1: Finding Outliers Using Quartiles (Part 2) (free trial)}

^{Strategy 1: The Constant k (free trial)}

^{Another Strategy for Finding Outliers (free trial)}

^{Deviation (free trial)}

^{Finding the Average Deviance (free trial)}

^{Step 2: Variance (free trial)}

^{Step 3: Standard Deviation (free trial)}

^{Strategy 2: Finding Outliers Using Standard Deviation (free trial)}

^{Mean Absolute Deviation (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 outliers and standard deviation.

It’s possible for a dataset to have extreme values, called outliers.

…Which can make some descriptive statistics misleading.

An outlier that is the result of an error is called an anomaly.

If an outlier is an anomaly, we should clean the data by removing it.

And if it isn’t, we need to leave it in, because it gives us important information, even if it skews our descriptive statistics.

To figure out if there are outliers in a data set, statisticians create cut-off values called fences.

Any data point lower than this… or greater than this… is an outlier.

Now, there are two strategies to determine where these fences should go.

One strategy is to use rules built from quartiles.

One for the lower fence.

[Q1-1.5(Q3-Q1), write formula on the lower fence]

And one for the upper fence.

[Q3 + 1.5 (Q3-Q1), write formula on the upper fence]

Where this is the interquartile range. [Q_3 – Q_1, replace by IQR]

[Q1-1.5(IQR)]

[Q3 + 1.5 (IQR)]

And this is a constant. [1.5]

…Which is often 1.5 but can vary, depending on the dataset.

A second strategy is to use rules in this form

Where this represents a measure of spread called the standard deviation. []

The standard deviation is the average distance between data points and the mean.

And to find the standard deviation of a dataset…

Start by finding all of the deviance scores, which is the distance between a given data point and the mean.

We can represent deviance scores using this notation.

Once we have the deviance scores for all data points..

Square them…

And add them.

We can also represent the sum of square deviations like this.

Finally, divide this by the total number of data points, [(x-x)2n] to find the variance. [variance=(x-x)2n]

Which is the standard deviation squared. [2=(x-x)2n]

So to find the standard deviation, just take the square root of this.[=(x-x)2n

Both standard deviation and variance are examples of measures of spread.

Now, it can take an unnecessarily long time to start by finding the sum of squared deviations.

Fortunately, there’s a shortcut we can use to find standard deviation.

First, calculate the total number of data points, the sum of all the data points, and the sum of squares.

Second, find the mean of the squares… and the square of the mean…

Third, use this formula to find the variance.

And take the square root if you want the standard deviation.

When the dataset is given in a frequency table, we can use the same shortcut to find the variance and standard deviation.

Though now, the number of data points is given by the sum of the frequency counts. [f]

And since we need to multiply each data point [highlight x] by its frequency count first [f], we represent the formula like this. [fx, fx2]

[2 =fx2f- (fxf)2 ]

And when the dataset is given in a grouped frequency table, we can only estimate the variance and standard deviation.

First, find the midpoints of each class interval.

Finally, in your exam, you could be asked to compare two data sets.

And in that case, you need to compare one measure of central location, and one measure of spread.

If the datasets don’t have outliers, use the mean and standard deviation.

But if there are outliers, the mean and standard deviation can be misleading, so it’s more appropriate to use the median and interquartile range.

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