How do box plots work

The first quartile marks one end of the box and the third quartile marks the other end of the box. The median or second quartile can be between the first and third quartiles, or it can be one, or the other, or both.

The box plot gives a good, quick picture of the data. You may encounter box-and-whisker plots that have dots marking outlier values. In those cases, the whiskers are not extending to the minimum and maximum values. The first quartile is two, the median is seven, and the third quartile is nine.

The smallest value is one, and the largest value is [latex] The following image shows the constructed box plot. The two whiskers extend from the first quartile to the smallest value and from the third quartile to the largest value.

The median is shown with a dashed line. It is important to start a box plot with a scaled number line. Otherwise the box plot may not be useful. Construct a box plot with the following properties; the calculator instructions for the minimum and maximum values as well as the quartiles follow the example. Arrow down and then use the right arrow key to go to the fifth picture, which is the box plot. Construct a box plot using a graphing calculator, and state the interquartile range.

For some sets of data, some of the largest value, smallest value, first quartile, median, and third quartile may be the same. For instance, you might have a data set in which the median and the third quartile are the same. In this case, the diagram would not have a dotted line inside the box displaying the median.

The right side of the box would display both the third quartile and the median. There are five data values ranging from Night class:. Graph a box-and-whisker plot for the data values shown. References Data from West Magazine. Chapter Review Box plots are a type of graph that can help visually organize data. Construct a box plot below. Use a ruler to measure and scale accurately.

Homework In a survey of year-olds in China, Germany, and the United States, people were asked the number of foreign countries they had visited in their lifetime. Given the following box plot, answer the questions. Answers will vary. Possible answer: State University conducted a survey to see how involved its students are in community service. The box plot shows the number of community service hours logged by participants over the past year.

Because the first and second quartiles are close, the data in this quarter is very similar. There is not much variation in the values. The data in the third quarter is much more variable, or spread out. This is clear because the second quartile is so far away from the third quartile.

Given the following box plots, answer the questions. Each box plot is spread out more in the greater values. The BMW 3 series is most likely to have an outlier. It has the longest whisker. Comparing the median ages, younger people tend to buy the BMW 3 series, while older people tend to buy the BMW 7 series.

However, this is not a rule, because there is so much variability in each data set. The second quarter has the smallest spread. There seems to be only a three-year difference between the first quartile and the median. The third quarter has the largest spread. There seems to be approximately a year difference between the median and the third quartile.

Each interval lies within a quarter, so we cannot tell exactly where the data in that quarter is concentrated. The interval from 31 to 35 years has the fewest data values. The results are as follows: of movies Frequency 0 5 1 9 2 6 3 4 4 1 Construct a box plot of the data. Their ages are as follows: Age Group Percent of Community 0—17 The bars will not be the same width for this example. Why not? What impact does this have on the reliability of the graph?

What percentage of the community is under age 35? Which box plot most resembles the information above? Follow this up by looking at the Items at a Glance reports. Obvious differences between box plots — see examples 1 and 2 , 1 and 3 , or 2 and 4. Any obvious difference between box plots for comparative groups is worthy of further investigation in the Items at a Glance reports.

Your school box plot is much higher or lower than the national reference group box plot. This also suggests an area of difference that could be explored further in the Items in Detail reports and through consultation. The 4 sections of the box plot are uneven in size — See example 1. This shows that many students have similar views at certain parts of the scale, but in other parts of the scale students are more variable in their views.

The long upper whisker in the example means that students views are varied amongst the most positive quartile group, and very similar for the least positive quartile group. The Items in Detail reports can be used to explore this further. Same median, different distribution — See examples 1 , 2 , and 3. The medians which generally will be close to the average are all at the same level.

However the box plots in these examples show very different distributions of views.