Data Visualization — Box Plot with Example

Today we are going to look at one of the most used data visualization plot called Box Plot that is used to find the distribution and five no. summary of our data.

Box plot:-

Introduction to Outliers

- An outlier is a value that lies in a data series which is either very small or large and thus affects the overall observation made from the data series. Outliers are usually treated as abnormal values that can affect the overall observation due to it's very high or low extremes values and hence should be discarded from the data series.

- As per the standards by all statisticians an outlier is a point which falls more than 1.5 times the interquartile range (IQR) above the third quartile (Q3) or below the first quartile (Q1).

• Outliers greatly influence the result.

Identifying Outliers

• let n be the no. of data values in the data set.
• The median (Q2) is the middle value of the data set.

• The Lower Quartile (Q1) is the median of the lower half of the data set

• The Upper quartile (Q3) is the median of the upper half of the data set.

• IQR is spread of the middle 50% of the data values.

Interquartile Range (IQR) = Upper Quartile (Q3) — Lower Quartile (Q1)

• Lower Limit = Q1–1.5 IQR.
• Upper Limit = Q3 + 1.5 IQR

• So any value that will be more than the upper limit or lesser than the lower limit will be the outliers. Only the data that lies within the Lower and upper limit are statistically considered normal and thus can be used for further observation or study.

Example:

Q. Let the data range be 199, 201, 236, 269,271,278,283,291, 301, 303, and 341

Ans. Here n = 11.

Hence in the data series 199, 201, 236, 269,271,278,283,291, 301, 303, 341, outliers are 199, 201 and 341. These 3 values which lie on either of the extremes can be considered abnormal and should be discarded from the entire series so that any analysis made on this series is not influenced by these extreme values.

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