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Beranda / The Followinf Data Represent Draw the Box Plot

The Followinf Data Represent Draw the Box Plot

Learning Outcomes

  • Display data graphically and interpret graphs: stemplots, histograms, and box plots.
  • Recognize, describe, and calculate the measures of location of data: quartiles and percentiles.

Box plots (also called box-and-whisker plots or box-whisker plots) requite a good graphical image of the concentration of the data. They also show how far the extreme values are from almost of the information. A box plot is constructed from five values: the minimum value, the first quartile, the median, the third quartile, and the maximum value. We utilize these values to compare how close other data values are to them.

To construct a box plot, use a horizontal or vertical number line and a rectangular box. The smallest and largest data values label the endpoints of the axis. The first quartile marks 1 end of the box and the third quartile marks the other finish of the box. Approximatelythe eye [latex]fifty[/latex] pct of the data fall within the box. The "whiskers" extend from the ends of the box to the smallest and largest data values. The median or second quartile tin can be betwixt the first and tertiary quartiles, or it can be one, or the other, or both. The box plot gives a adept, quick picture of the information.

Note

You lot 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.

Consider, again, this dataset.

[latex]1[/latex], [latex]1[/latex], [latex]two[/latex], [latex]2[/latex], [latex]iv[/latex], [latex]half dozen[/latex], [latex]half dozen.8[/latex], [latex]7.two[/latex], [latex]8[/latex], [latex]viii.three[/latex], [latex]nine[/latex], [latex]10[/latex], [latex]ten[/latex], [latex]11.5[/latex]

The outset quartile is two, the median is 7, and the tertiary quartile is nine. The smallest value is one, and the largest value is [latex]eleven.five[/latex]. The post-obit prototype shows the constructed box plot.

Note

Run across the calculator instructions on the TI web site.

Horizontal boxplot's first whisker extends from the smallest value, 1, to the first quartile, 2, the box begins at the first quartile and extends to the third quartile, 9, a vertical dashed line is drawn at the median, 7, and the second whisker extends from the third quartile to the largest value of 11.5.

The two whiskers extend from the showtime quartile to the smallest value and from the tertiary quartile to the largest value. The median is shown with a dashed line.

Note

It is of import to start a box plot with ascaled number line. Otherwise the box plot may not be useful.

Example

The following data are the heights of [latex]twoscore[/latex] students in a statistics class.

[latex]59[/latex]; [latex]60[/latex]; [latex]61[/latex]; [latex]62[/latex]; [latex]62[/latex]; [latex]63[/latex]; [latex]63[/latex]; [latex]64[/latex]; [latex]64[/latex]; [latex]64[/latex]; [latex]65[/latex]; [latex]65[/latex]; [latex]65[/latex]; [latex]65[/latex]; [latex]65[/latex]; [latex]65[/latex]; [latex]65[/latex]; [latex]65[/latex]; [latex]65[/latex]; [latex]66[/latex]; [latex]66[/latex]; [latex]67[/latex]; [latex]67[/latex]; [latex]68[/latex]; [latex]68[/latex]; [latex]69[/latex]; [latex]seventy[/latex]; [latex]lxx[/latex]; [latex]lxx[/latex]; [latex]70[/latex]; [latex]70[/latex]; [latex]71[/latex]; [latex]71[/latex]; [latex]72[/latex]; [latex]72[/latex]; [latex]73[/latex]; [latex]74[/latex]; [latex]74[/latex]; [latex]75[/latex]; [latex]77[/latex]

Construct a box plot with the following properties; the reckoner instructions for the minimum and maximum values every bit well as the quartiles follow the example.

  • Minimum value = [latex]59[/latex]
  • Maximum value = [latex]77[/latex]
  • Q1: Offset quartile = [latex]64.5[/latex]
  • Q2: Second quartile or median= [latex]66[/latex]
  • Q3: Third quartile = [latex]seventy[/latex]
Horizontal boxplot with first whisker extending from smallest value, 59, to Q1, 64.5, box beginning from Q1 to Q3, 70, median dashed line at Q2, 66, and second whisker extending from Q3 to largest value, 77.
  1. Each quarter has approximately [latex]25[/latex]% of the information.
  2. The spreads of the iv quarters are [latex]64.5 – 59 = v.5[/latex] (outset quarter), [latex]66 – 64.five = 1.five[/latex] (second quarter), [latex]lxx – 66 = 4[/latex] (third quarter), and [latex]77 – seventy = 7[/latex] (fourth quarter). So, the second quarter has the smallest spread and the fourth quarter has the largest spread.
  3. Range = maximum value – the minimum value = 77 – 59 = 18
  4. Interquartile Range: [latex]IQR[/latex] = [latex]Q_3[/latex] – [latex]Q_1[/latex] = [latex]70 – 64.v = 5.5[/latex].
  5. The interval [latex]59–65[/latex] has more than [latex]25[/latex]% of the data and so it has more than data in it than the interval [latex]66[/latex] through [latex]seventy[/latex] which has [latex]25[/latex]% of the data.
  6. The center [latex]50[/latex]% (middle one-half) of the information has a range of [latex]5.5[/latex] inches.

USING THE TI-83, 83+, 84, 84+ Calculator

To discover the minimum, maximum, and quartiles:

Enter data into the list editor (Pres STAT 1:EDIT). If you need to clear the list, arrow up to the name L1, press Clear, and and then arrow down.

Put the data values into the list L1.

Press STAT and arrow to CALC. Printing one:1-VarStats. Enter L1.

Printing ENTER.

Apply the down and upward arrow keys to scroll.

Smallest value = [latex]59[/latex].

Largest value = [latex]77[/latex].

[latex]Q_1[/latex]: Commencement quartile = [latex]64.v[/latex].

[latex]Q_2[/latex]: Second quartile or median = [latex]66[/latex].

[latex]Q_3[/latex]: Third quartile = [latex]70[/latex].

To construct the box plot:

Printing 4:Plotsoff. Press ENTER.

Arrow down and then apply the right arrow key to get to the fifth picture, which is the box plot. Press ENTER.

Arrow downwards to Xlist: Press 2nd ane for L1

Pointer downwards to Freq: Press ALPHA. Printing 1.

Printing Zoom. Press 9: ZoomStat.

Press TRACE, and apply the arrow keys to examine the box plot.

Try It

The following data are the number of pages in [latex]40[/latex] books on a shelf. Construct a box plot using a graphing calculator, and state the interquartile range.

[latex]136[/latex]; [latex]140[/latex]; [latex]178[/latex]; [latex]190[/latex]; [latex]205[/latex]; [latex]215[/latex]; [latex]217[/latex]; [latex]218[/latex]; [latex]232[/latex]; [latex]234[/latex]; [latex]240[/latex]; [latex]255[/latex]; [latex]270[/latex]; [latex]275[/latex]; [latex]290[/latex]; [latex]301[/latex]; [latex]303[/latex]; [latex]315[/latex]; [latex]317[/latex]; [latex]318[/latex]; [latex]326[/latex]; [latex]333[/latex]; [latex]343[/latex]; [latex]349[/latex]; [latex]360[/latex]; [latex]369[/latex]; [latex]377[/latex]; [latex]388[/latex]; [latex]391[/latex]; [latex]392[/latex]; [latex]398[/latex]; [latex]400[/latex]; [latex]402[/latex]; [latex]405[/latex]; [latex]408[/latex]; [latex]422[/latex]; [latex]429[/latex]; [latex]450[/latex]; [latex]475[/latex]; [latex]512[/latex]

This video explains what descriptive statistics are needed to create a box and whisker plot.

For some sets of information, some of the largest value, smallest value, first quartile, median, and third quartile may be the aforementioned. For instance, y'all might have a data prepare in which the median and the third quartile are the same. In this instance, the diagram would not have a dotted line within the box displaying the median. The correct side of the box would display both the third quartile and the median. For instance, if the smallest value and the get-go quartile were both one, the median and the third quartile were both five, and the largest value was seven, the box plot would expect like:

Horizontal boxplot box begins at the smallest value and Q1, 1, until the Q3 and median, 5, no median line is designated, and has its lone whisker extending from the Q3 to the largest value, 7.

In this case, at least [latex]25[/latex]% of the values are equal to 1. 20-five percent of the values are between one and five, inclusive. At least [latex]25[/latex]% of the values are equal to 5. The top [latex]25[/latex]% of the values fall betwixt five and seven, inclusive.

Case

Test scores for a college statistics form held during the day are:

[latex]99[/latex]; [latex]56[/latex]; [latex]78[/latex]; [latex]55.5[/latex]; [latex]32[/latex]; [latex]ninety[/latex]; [latex]eighty[/latex]; [latex]81[/latex]; [latex]56[/latex]; [latex]59[/latex]; [latex]45[/latex]; [latex]77[/latex]; [latex]84.5[/latex]; [latex]84[/latex]; [latex]lxx[/latex]; [latex]72[/latex]; [latex]68[/latex]; [latex]32[/latex]; [latex]79[/latex]; [latex]90[/latex]

Exam scores for a college statistics grade held during the evening are:

[latex]98[/latex]; [latex]78[/latex]; [latex]68[/latex]; [latex]83[/latex]; [latex]81[/latex]; [latex]89[/latex]; [latex]88[/latex]; [latex]76[/latex]; [latex]65[/latex]; [latex]45[/latex]; [latex]98[/latex]; [latex]90[/latex]; [latex]80[/latex]; [latex]84.five[/latex]; [latex]85[/latex]; [latex]79[/latex]; [latex]78[/latex]; [latex]98[/latex]; [latex]90[/latex]; [latex]79[/latex]; [latex]81[/latex]; [latex]25.5[/latex]

  1. Find the smallest and largest values, the median, and the offset and 3rd quartile for the twenty-four hour period class.
  2. Find the smallest and largest values, the median, and the showtime and third quartile for the nighttime class.
  3. For each data set up, what percentage of the data is between the smallest value and the offset quartile? the kickoff quartile and the median? the median and the tertiary quartile? the tertiary quartile and the largest value? What percentage of the data is between the commencement quartile and the largest value?
  4. Create a box plot for each set of data. Employ 1 number line for both box plots.
  5. Which box plot has the widest spread for the middle [latex]50[/latex]% of the data (the data between the showtime and third quartiles)? What does this hateful for that set up of data in comparison to the other set of data?

Attempt It

The following data prepare shows the heights in inches for the boys in a class of [latex]40[/latex] students.

[latex]66[/latex]; [latex]66[/latex]; [latex]67[/latex]; [latex]67[/latex]; [latex]68[/latex]; [latex]68[/latex]; [latex]68[/latex]; [latex]68[/latex]; [latex]68[/latex]; [latex]69[/latex]; [latex]69[/latex]; [latex]69[/latex]; [latex]seventy[/latex]; [latex]71[/latex]; [latex]72[/latex]; [latex]72[/latex]; [latex]72[/latex]; [latex]73[/latex]; [latex]73[/latex]; [latex]74[/latex]

The post-obit data set shows the heights in inches for the girls in a class of [latex]forty[/latex] students.

[latex]61[/latex]; [latex]61[/latex]; [latex]62[/latex]; [latex]62[/latex]; [latex]63[/latex]; [latex]63[/latex]; [latex]63[/latex]; [latex]65[/latex]; [latex]65[/latex]; [latex]65[/latex]; [latex]66[/latex]; [latex]66[/latex]; [latex]66[/latex]; [latex]67[/latex]; [latex]68[/latex]; [latex]68[/latex]; [latex]68[/latex]; [latex]69[/latex]; [latex]69[/latex]; [latex]69[/latex]

Construct a box plot using a graphing calculator for each data set, and state which box plot has the wider spread for the centre [latex]50[/latex]% of the data.

example

Graph a box-and-whisker plot for the data values shown.

[latex]10[/latex]; [latex]x[/latex]; [latex]10[/latex]; [latex]15[/latex]; [latex]35[/latex]; [latex]75[/latex]; [latex]xc[/latex]; [latex]95[/latex]; [latex]100[/latex]; [latex]175[/latex]; [latex]420[/latex]; [latex]490[/latex]; [latex]515[/latex]; [latex]515[/latex]; [latex]790[/latex]

The five numbers used to create a box-and-whisker plot are:

  • Min: [latex]x[/latex]
  • [latex]Q_1[/latex]: [latex]fifteen[/latex]
  • Med: [latex]95[/latex]
  • [latex]Q_3[/latex]: [latex]490[/latex]
  • Max: [latex]790[/latex]

The following graph shows the box-and-whisker plot.

Endeavor Information technology

Follow the steps you lot used to graph a box-and-whisker plot for the information values shown.

[latex]0[/latex]; [latex]5[/latex]; [latex]five[/latex]; [latex]15[/latex]; [latex]30[/latex]; [latex]thirty[/latex]; [latex]45[/latex]; [latex]l[/latex]; [latex]50[/latex]; [latex]60[/latex]; [latex]75[/latex]; [latex]110[/latex]; [latex]140[/latex]; [latex]240[/latex]; [latex]330[/latex]

Concept Review

Box plots are a type of graph that tin can help visually organize data. To graph a box plot the following data points must be calculated: the minimum value, the kickoff quartile, the median, the 3rd quartile, and the maximum value. Once the box plot is graphed, yous can display and compare distributions of information.

References

Information from Due west Mag.

Additional Resources

Use the online imathAS box plot tool to create box and whisker plots.

makeup898.blogspot.com

Source: https://courses.lumenlearning.com/introstats1/chapter/box-plots/