Presentation on theme: "Five Number Summary and Box Plots"— Presentation transcript:
1Five Number Summary and Box Plots Please view this tutorial and answer the follow-up questions on loose leaf to be handed into your teacher.
2Five Number Summary and Box Plot Basics The Five Number Summary consists of the minimum, lower quartile (Q1), median, upper quartile (Q3), and maximum.It is used to determine the variability (or the differences in data) of a data set and to construct box plots.Box plots are used as a visual representation of the data.
3Five Number Summary Definitions Minimum: the smallest value in a data setLower quartile (Q1): the 25th percentile; 25% of the information is less than this valueMedian: the 50th percentile or middle valueUpper quartile (Q3): the 75th percentile; 75% of the information is less than this valueMaximum: the largest value in a data set
4Example Next, you’ll break up this information into quarters. There will be the same amount of numbers in each section.5678910111518192024
5Example First, find the middle number. 5678910111518192024Since this list has 13 values, the middle number would be the 7th number.Note: If there was an even amount of values, you would find the average of the two middle numbers.
6ExampleNow that you have your halfway point, find the middle of the top and bottom sections.5678910111518192024There are six values in the top section so the middle value would fall between the 3rd and 4th values.Find the middle value for the bottom section.
7Example The middle value would fall between the 10th and 11th values. 5678910111518192024Now that we have our intervals set up, we can find the values for our five number summary.
8ExampleThe minimum is 5.5678910111518192024To find the lower quartile (Q1), find the average of 7 and 8.Q1 is 7.5.The median, or middle value is 10.To find the upper quartile (Q3), find the average of 18 and 19.Q is 18.5.The maximum is 24.
9ExampleYou would write the five number summary for this data set as follows:minimum= 5Q1 = 7.5median= 10Q3 = 18.5maximum= 245678910111518192024
10Five Number Summary on the Calculator To find the five number summary on the calculator, first you need to enter your information into a list then quit.
11Five Number Summary on the Calculator Next, hit STAT then go over to CALC then to 1:1VarStats( then hit Enter.
12Five Number Summary on the Calculator Tell the calculator where your information is (ex. L1) then hit ENTERScroll down to seethe five numbersummary.
13Making a Box PlotUsing the five number summary, you can easily construct a box plot.minimum= 5Q1 = 7.5median= 10Q3 = 18.5maximum= 24First, we need to make a number line.Choose your minimum, maximum and scale based on your five number summary.Our minimum is 5 and maximum is 24. What should we choose as our minimum, maximum and scale for our number line?
14Making a Box Plot0 would be a good choice for our minimum, 25 for our maximum with a scale of 5.minimum= 5Q1 = 7.5median= 10Q3 = 18.5maximum= 24Next, we need to mark off the values for each number in the five number summary.510152025
15Making a Box Plot Make a small tick mark for the minimum and maximum. Q1 = 7.5median= 10Q3 = 18.5maximum= 24Make larger tick marks for Q1, median, and Q3.510152025
16Making a Box PlotConnect the longer tick marks with two lines to form a box.minimum= 5Q1 = 7.5median= 10Q3 = 18.5maximum= 24Connect the smaller tick marks with lines to the center of the box.510152025
17Describing a Box PlotIn a box plot, each segment represents 25% of the information.minimum= 5Q1 = 7.5median= 10Q3 = 18.5maximum= 2425%25%25%25%What can you tell about the way the information is grouped based on this histogram?510152025
18Describing a Box PlotIntervals that are smaller (like from the minimum to Q1) have information that is tightly packed together.minimum= 5Q1 = 7.5median= 10Q3 = 18.5maximum= 2425%25%25%25%Intervals that are larger (like from the median to Q3) have information that is more spread out.510152025
19Describing a Box PlotThe length of the box (from Q1 to Q3) represents the IQR, or interquartile range. This is the middle 50% of the data.minimum= 5Q1 = 7.5median= 10Q3 = 18.5maximum= 2450%This value will help you determine the variability of a data set or to compare variability of more than one set of data.510152025
20Describing a Box PlotThe larger the IQR, the larger the variability of the data set. The smaller the IQR, the smaller the variability. The IQR for this box plot is 11 (Q3-Q1).minimum= 5Q1 = 7.5median= 10Q3 = 18.5maximum= 2450%You can also look at the length of the box to help determine the variability of the data.510152025
21Describing a Box PlotSo along with the five number summary, you can also talk about whether the box plot is skewed or symmetric based on the size of each interval.minimum= 5Q1 = 7.5median= 10Q3 = 18.5maximum= 24Do you think this box plot is skewed right, skewed left, or symmetric?510152025
22Describing a Box PlotThis box plot is skewed to the right because the intervals between the median and Q3 and the interval between Q3 and the maximum are very spread out.Sometimes it helps to compare the box plot to a histogram to determine the skewness of the plot.510152025
23Describing a Box PlotNotice that the histogram is skewed to the right (the tail is on the right).510152025510152025
24Describing a Box PlotHere is the correct description of this box plot.minimum= 5Q1 = 7.5median= 10Q3 = 18.5maximum= 24IQR = 11range = 19skewed to the right510152025
25Follow Up QuestionsAnswer the following questions on loose leaf and hand them in to your teacher.
26Find the five number summary for this data set. The following are scores from 25 students on a unit test in mathematics.7592627885779365809050705798455473846074Find the five number summary for this data set.Find the interquartile range (IQR).Make a box plot for this information.Describe the distribution.
275060708090100About what percentage of students scored between 70 and 90 on the test depicted in the box plot above?40507590Cannot be determined from the information given