Which Box-and-whisker Plot Represents The Data 13 43

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Amalgam box and whisker plots

Example one – Box and whisker plots
Summary

A box and whisker plot (sometimes called a boxplot) is a graph that presents information from a v-number summary. It does non testify a distribution in as much item as a stem and leaf plot or histogram does, just is especially useful for indicating whether a distribution is skewed and whether there are potential unusual observations (outliers) in the data set. Box and whisker plots are too very useful when large numbers of observations are involved and when 2 or more data sets are beingness compared. (See the section on v-number summaries for more information.)

Box and whisker plots are ideal for comparison distributions because the middle, spread and overall range are immediately apparent.

A general example of a box and whisker plot.

A box and whisker plot is a way of summarizing a set of information measured on an interval scale. It is often used in explanatory information analysis. This type of graph is used to show the shape of the distribution, its central value, and its variability.

In a box and whisker plot:

the ends of the box are the upper and lower quartiles, so the box spans the interquartile range
the median is marked by a vertical line inside the box
the whiskers are the ii lines exterior the box that extend to the highest and lowest observations.

Figure 1. A breakdown of the various components that make up a box and whisker plot.

Example 1 – Box and whisker plots

Like Angela, Carl works at a reckoner store. He as well recorded the number of sales he made each calendar month. In the past 12 months, he sold the following numbers of computers:

51, 17, 25, 39, vii, 49, 62, 41, 20, 6, 43, thirteen.

Requite a five-number summary of Carl's and Angela's sales.
Make two box and whisker plots, one for Angela'due south sales and one for Carl's.
Briefly describe the comparisons betwixt their sales.

Answers

Commencement, put the data in ascending order. Then observe the median.
6, 7, thirteen, 17, 20, 25, 39, 41, 43, 49, 51, 62.
Median = (12th + 1st) ÷ two = 6.fifth value
= (sixth + seventh observations) ÷ 2
= (25 + 39) ÷ ii
= 32

There are six numbers below the median, namely: 6, vii, xiii, 17, 20, 25.
Q1 = the median of these half-dozen items
= (vi + 1 ) ÷ two= three.five^th value
= (third + fourth observations) ÷ 2
= (13 + 17) ÷ 2
= 15

Here are six numbers higher up the median, namely: 39, 41, 43, 49, 51, 62.
Q₃ = the median of these six items
= (6 + 1) ÷ 2= 3.5^th value
= (tertiary + fourth observations) ÷ 2
= 46

The v-number summary for Carl'south sales is 6, 15, 32, 46, 62.

Using the same calculations, we can make up one's mind that the five-number summary for Angela is 1, 17, 26, 42, 57.
Please note that box and whisker plots tin can exist drawn either vertically or horizontally.
Carl's highest and lowest sales are both higher than Angela's corresponding sales, and Carl'southward median sales figure is higher than Angela'southward. Also, Carl's interquartile range is larger than Angela's.
These results advise that Carl consistently sells more computers than Angela does.

Summary

There are several means to describe the centre and spread of a distribution. One manner to present this data is with a v-number summary. Information technology uses the median equally its eye value and gives a brief picture of the other important distribution values. Another measure out of spread uses the mean and standard departure to decipher the spread of data. This technique, all the same, is all-time used with symmetrical distributions with no outliers.

Despite this restriction, the mean and standard deviation measures are used more than commonly than the five-number summary. The reason for this is that many natural phenomena tin can be approximately described by a normal distribution. And for normal distributions, the mean and standard deviation are the best measures of centre and spread respectively.

Standard deviation takes every value into account, has extremely useful properties when used with a normal distribution, and is mathematically manageable. Only the standard deviation is non a adept measure of spread in highly skewed distributions and, in these instances, should be supplemented by other measures such as the semi-quartile range.

The semi-quartile range is rarely used every bit a measure of spread, partly considering information technology is non as manageable every bit others. Still, information technology is a useful statistic because it is less influenced by extreme values than the standard deviation, is less subject to sampling fluctuations in highly skewed distributions and is limited to only ii values Q₁ and Q₃. Withal, it cannot stand alone as a measure of spread.