To recognize box-and-whisker plots, you have to understand medians and also quartiles the a data set.

The mean is the middle number of a collection of data, or the mean of the two middle numbers (if there are an even variety of data points).

The median ( Q 2 ) divides the data set into two parts, the upper set and the reduced set. The lower quartile ( Q 1 ) is the average of the reduced half, and the top quartile ( Q 3 ) is the average of the top half.

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Example:

uncover Q 1 , Q 2 , and also Q 3 for the complying with data set, and draw a box-and-whisker plot.

2 , 6 , 7 , 8 , 8 , 11 , 12 , 13 , 14 , 15 , 22 , 23

There are 12 data points. The center two room 11 and 12 . Therefore the median, Q 2 , is 11.5 .

The "lower half" of the data set is the set 2 , 6 , 7 , 8 , 8 , 11 . The median right here is 7.5 . So Q 1 = 7.5 .

The "upper half" of the data collection is the collection 12 , 13 , 14 , 15 , 22 , 23 . The median below is 14.5 . For this reason Q 3 = 14.5 .

A box-and-whisker plot screens the values Q 1 , Q 2 , and also Q 3 , in addition to the excessive values the the data collection ( 2 and 23 , in this case): A box & whisker plot mirrors a "box" through left edge at Q 1 , appropriate edge in ~ Q 3 , the "middle" of the box at Q 2 (the median) and also the maximum and minimum as "whiskers".

keep in mind that the plot divides the data right into 4 equal parts. The left whisker to represent the bottom 25 % the the data, the left half of the box represents the 2nd 25 % , the right fifty percent of package represents the third 25 % , and the ideal whisker to represent the peak 25 % .

## Outliers

If a data value is very far far from the quartiles (either much much less than Q 1 or much greater than Q 3 ), it is sometimes designated an outlier . Rather of being shown using the whiskers the the box-and-whisker plot, outliers space usually presented as independently plotted points. The standard meaning for an outlier is a number which is much less than Q 1 or greater than Q 3 by more than 1.5 times the interquartile variety ( IQR = Q 3 − Q 1 ). That is, one outlier is any type of number less than Q 1 − ( 1.5 × IQR ) or better than Q 3 + ( 1.5 × IQR ) .

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Example:

find Q 1 , Q 2 , and Q 3 because that the following data set. Identify any outliers, and also draw a box-and-whisker plot.

5 , 40 , 42 , 46 , 48 , 49 , 50 , 50 , 52 , 53 , 55 , 56 , 58 , 75 , 102

There room 15 values, i ordered it in increasing order. So, Q 2 is the 8 th data point, 50 .

Q 1 is the 4 th data point, 46 , and also Q 3 is the 12 th data point, 56 .

The interquartile variety IQR is Q 3 − Q 1 or 56 − 47 = 10 .

now we require to find whether there space values less than Q 1 − ( 1.5 × IQR ) or better than Q 3 + ( 1.5 × IQR ) .

Q 1 − ( 1.5 × IQR ) = 46 − 15 = 31

Q 3 + ( 1.5 × IQR ) = 56 + 15 = 71

due to the fact that 5 is much less than 31 and 75 and 102 are higher than 71 , there space 3 outliers.

The box-and-whisker plot is together shown. Keep in mind that 40 and also 58 are presented as the ends of the whiskers, v the outliers plotted separately.