Box Plots and Simple Interest

Box Plots

Today we will be learning about how we can sample populations and make inferences from the findings about the total population.

Learning Objective

I can make inferences using random samples about the whole population.

​Learning Standards:

• ​7.SP.2 - Use data from a random sample about an unknown characteristic of a population. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions, i.e., generate a sampling distribution.

• 7.SP.4 - Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

Chapter 8 Vocabulary

​Vocabulary

​Click the hyperlink to get started.

​When finished learning the vocabulary proceed to the next slide.

Match

Match the following

• A statistical prediction.

• A way of displaying data that is much like a bar graph in that the height of the bars is proportional to the number of elements.  The difference is that each bar of a histogram represents the number of data elements in a range of values, such as the number of people who weigh from 100 pounds up to, but not including, 120 pounds.  Each range of values should have the same width.

• A graphic way of showing a summary of data using the median, quartiles, and extremes of the data.

• A way to visually compare multiple data distributions by drawing each of their box plots on the same axis.

• A collection of objects or group of people about whom information is gathered.

inference

histogram

box plot

parallel box plot

population

• inference

• histogram

• box plot

• parallel box plot

• population

Match

Match the following

• A subset (group) of a given population with the same characteristics as the whole population.

• A subgroup of the population that has the similar characteristic of interest as that of the whole population.  Representative samples are usually the result of random sampling.

• A sample which was chosen as a result of a random process.  A random sample can represent the whole population well. 

• When dealing with measures of center, it is often useful to consider the distribution of the data.  For symmetric distributions with no outliers, the mean can represent the middle, or “typical” value, of the data well.  However, in the presence of outliers or non-symmetrical data distributions, the median may be a better measure.  Also see mean and median.

• A measure of the amount of variability in a data set. Three ways to measure spread are the range, the mean absolute deviation, and the interquartile range.

sample

representative sample

random sample

center (center of a data distribution)

spread

• sample

• representative sample

• random sample

• center (center of a data distribution)

• spread

Match

Match the following

• The mean, or average, of several numbers is one way of defining the “middle” of the numbers. To find the average of a group of numbers, add the numbers together then divide by the number of numbers in the set.  For example, the average of the numbers 1, 5, and 6 is (1+5+6)÷3=4.  The mean is generally the best measure of central tendency when there are not outliers in the data set.

• The sum of given values divided by the number of values used in computing the sum.  For example, the average of 1, 4, and 10 is (1+4+10) ÷ 3 = 5. 

• The middle number of an ordered set of data. If there is no distinct middle, then the average of the two middle numbers is the median. The median is generally more accurate than the mean as a measure of central tendency when there are outliers in the data set.

• A way to measure the spread of data. It is calculated by subtracting the first quartile from the third quartile.

• The range of a set of data is the difference between the highest and lowest values.

mean

average

median

IQR (Interquartile Range)

range

• mean

• average

• median

• IQR (Interquartile Range)

• range

Let's learn about Box Plots!

​A box plot (sometimes called a “box-and-whisker plot”) displays a summary of data using the median, quartiles, and extremes of the data.  The box contains “the middle half” of the data.  The right segment represents the top 25% of the data, and the left segment represents the bottom 25% of the data.  A box plot makes it easy to see where the data are spread out and where they are concentrated.  The larger the box, the more the data are spread out.

To construct a box plot using a number line that shows the range of the data, draw vertical line segments above the median, first quartile, and third quartile.  Then connect the lines from the first and third quartiles to form a rectangle.  Place a vertical line segment above the number line at the highest and lowest data values.  Connect the minimum value to the first quartile and the maximum value to the third quartile using horizontal segments.  The box plot is shown below for the data set 2, 7, 9, 12, 14, 22, 32, 36, and 43.

Match

Match the answers to the appropriate label.

• Upper Extreme

• Lower Extreme

• Median

• Upper Quartile

• Lower Quartile

28

22

26

27

24

• 28

• 22

• 26

• 27

• 24

Match

Match the answers to the appropriate label.

• Upper Extreme

• Lower Extreme

• Median

• Upper Quartile

• Lower Quartile

50

10

30

40

15

• 50

• 10

• 30

• 40

• 15

Match

Match the answers to the appropriate label.

• Upper Extreme

• Lower Extreme

• Median

• Upper Quartile

• Lower Quartile

10

3

7

8

6

• 10

• 3

• 7

• 8

• 6

Match

Match the answers to the appropriate label.

• Upper Extreme

• Lower Extreme

• Median

• Upper Quartile

• Lower Quartile

72

35

58

65

39

• 72

• 35

• 58

• 65

• 39

Match

Match the answers to the appropriate label.

• Upper Extreme

• Lower Extreme

• Median

• Upper Quartile

• Lower Quartile

91

0

62

83

18

• 91

• 0

• 62

• 83

• 18

Match

Match the numbers to answer the questions.

• What was the highest total points scored?

• What was the lowest total points scored?

• What was the median number of points scored?

• What percent of games did Robinson score 19 or more points?

• What percent of games did Robinson score 13 points or fewer?

36

8

19

50%

25%

• 36

• 8

• 19

• 50%

• 25%

Open Ended

How many points do you think Robinson will score in his next game and why?

Match

Match the numbers to answer the questions.

• What is the largest number of songs in a playlist?

• What is the smallest number of songs in a playlist?

• What is the median number of songs in a playlist?

• What percent of playlists have 22 or more songs?

• What is the range of the number of songs in the middle 50% of playlists?

185

3

43

75%

37

• 185

• 3

• 43

• 75%

• 37

Open Ended

Is it more likely that a playlist will have more than 40 songs or fewer than 20 songs? Explain your answer.

The next step

Complete the following after clicking on the link in the next slide. (Exit Ticket)

• Reasonable Samples (Video)

• Valid Claims (practice)

• Making inferences from random samples (practice)

• Comparing distributions with dot plots (Video)

• Comparing distributions (practice)

​Khan Academy
Unit 7
Lesson 4: Comparing and sampling populations.

Reasonable samples (video) | Khan Academy

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