Identify outliers for the following dataset and draw the box-and whisker plot. 7,8,13,16,16,17,17,18,18,19,19,20,20,21,26,30,32
To identify outliers in a dataset, we first need to calculate the IQR (interquartile range) and determine the lower and upper bounds.
Dataset: 7, 8, 13, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 26, 30, 32
Sorted dataset: 7, 8, 13, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 26, 30, 32
Q1 = 16
Q3 = 20
IQR = Q3 - Q1 = 20 - 16 = 4
Lower bound = Q1 - 1.5*IQR = 16 - 1.5*4 = 16 - 6 = 10
Upper bound = Q3 + 1.5*IQR = 20 + 1.5*4 = 20 + 6 = 26
Any data point that is below the lower bound or above the upper bound is considered an outlier.
The outliers in the dataset are 7 and 32.
The box-and-whisker plot will have a box from Q1 to Q3, with a line through the box to represent the median. Whiskers extend from the box to the lowest and highest non-outlier data points, and any outliers are plotted as individual points.
Box-and-whisker plot for the dataset:
| *
| -
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7 13 16 17 18 20 21 30 32
In the boxplot, the box represents the interquartile range (IQR), the line in the box represents the median, the whiskers represent the lowest and highest non-outlier data points, and the outliers are plotted as individual points.