Data Analysis Quest

4/15 Quest Lesson:

Interpreting and Analyzing Data Sets and Data Displays

Learning Objective:

I can describe and interpret data sets and data displays.

Multiple Choice

Which of the following is a statistical question?

• What is the name of the first president of Yale University?

• What is the color of the sky?
• What is the average height of students in a school?
• How many planets are in the solar system?
• What is the capital of France?

Multiple Select

Which of the following are statistical questions? Select all that apply.

• Did NBA teams score more points per game in 1997 or 2025?

• How tall is the tallest 6th grader in the world?

• How much money did Ryan Smith make last year?

• What were the most popular movies during each decade since 1950?

• How many games did the Nuggets win with Michael Malone as coach?

​Dot or Line Plot

​Frequency Table

​Histogram

​Box Plot

Match

Match each type of data display with its name:

Histogram

Box Plots

Frequency Table

Dot or Line Plot

Bar Graph

• Histogram

• Box Plots

• Frequency Table

• Dot or Line Plot

• Bar Graph

Skewed Left or Right

• When a distribution is skewed left the mean is less than the median

• When a distribution is skewed right the mean will be more than the median.

Uniform Distribution

• In a uniform distribution, the data values are spread out equally among the intervals.

• The values are the same or close to the same.

• The data is distributed evenly around the mean and the mean and the median are close to the same.

Bell or Symmetrical Distributions

• Symmetrical distributions of data can also be called normal or bell shaped.

• Since their distribution is fairly normal, the mean and the median will be close to the same.

Multiple Choice

Which of the following best describes the shape of the distribution?

• SKEWED LEFT
• SKEWED RIGHT
• UNIFORM
• SYMMETRICAL

Multiple Choice

Which of the following best describes the shape of the distribution?

• SKEWED LEFT
• SKEWED RIGHT
• UNIFORM
• SYMMETRICAL

Multiple Choice

Which of the following best describes the shape of the distribution?

• SKEWED LEFT
• SKEWED RIGHT
• UNIFORM
• SYMMETRICAL

Multiple Choice

Describe the shape of the distribution.

• Symmetrical

• Skewed Left

• Skewed Right

• Uniform

Multiple Choice

Describe the shape of the distribution.

• Symmetrical

• Skewed Left

• Skewed Right

• Uniform

Multiple Choice

Which best describes the distribution of the data?

• Skewed Left

• Skewed Right

• Uniform

• Approximately Symmetrical

Multiple Choice

Which best describes the distribution of this data?

• Skewed Left

• Skewed Right

• Uniform

• Symmetrical

Multiple Choice

How many students took the quiz? (count the dots)

• 15

• 20

• 12

• 17

• 108

Multiple Choice

What is the outlier of the data set?

• 88%

• 93%

• 98%

• No Outliers

Multiple Choice

What is the mode? 

• 88%

• 93%

• 98%

• 89%

• 92%

Multiple Select

Which two of the following are gaps in the data distribution?

• 88%

• 99%

• 96%

• 100%

• 92%

Multiple Choice

What is the MODE of this data?

• 90
• 85, 90, and 95
• 85 and 95
• None

Multiple Choice

What is the range of the test scores?

• 15
• 100
• 6
• 10
• 12

Multiple Choice

What is the highest score in the class?

• 88%

• 100%

• 13

• 98%

Multiple Choice

Which kind of display uses intervals to display data?

• Box Plot

• Histogram

• Both

• Neither

Multiple Choice

What kind of display shows the data in quartiles?

• Box plot

• Histogram

• Dot Plot

• All types of graphs

Multiple Choice

The frequency table shows the times (in seconds) that it takes for several students to run 40 yards.

Which histogram correctly displays the data?

Multiple Choice

The histogram shows the ages of the customers in a grocery store.

Which frequency chart could be best represented by the histogram?

Multiple Choice

What is the median?

• 62
• 58
• 66
• 60

Multiple Choice

Which box and whisker plot best represents the data set?

Important Terms

• Data: information in number form

• Frequency: How often something happens

• Outliers: a piece of data that has a value much less than or much greater than the rest of the data

• Range: The difference between the minimum value and the maximum value in a data set.

• Minimum: the piece of data that has the least value in a set of data.

• Maximum: the piece of data that has the most value in a data set.

​Dot Plot

​Organizes a set of data on a number line. Shows individual values.

Dot Plots

• Displays the frequency (how often) of each data value in a data set.

• Sometimes called a line plot

• The total number of x's or dots equals the total number of data values in the set of data.

Multiple Choice

What day were the least amount of cars sold?

• Monday

• Tuesday

• Thursday

• Saturday

Multiple Choice

The dot plot show the distances, in miles cyclists completed on Saturday. How many cyclists went at least 11 miles?

• 10

• 1

• 3

Histograms

• A histogram is a graphical display of data using bars of different heights.

• In a histogram, each bar groups numbers into intervals or ranges or numbers.

Histograms can tell us:

• Mode

• Frequency

• Intervals

To Construct a Histogram

Represent the frequency (how many data points in the interval) on the y-axis and the intervals on the x-axis.

Using the frequencies as the heights, draw the vertical bars for each class.

Multiple Choice

Which interval contains exactly 4 students?

• 56-59

• 60-63

• 60-67

• 48-51

• 52-55

Multiple Choice

Describe the shape of the data distribution:

• Skewed Left

• Skewed Right

• Symmetrical

• Approximately Symmetrical

• Uniform

Multiple Choice

Which histogram matches the data set? (Hint: the greatest number 49.)

Box Plot

• A box plot—also called a box and whisker plot—displays the five-number summary of a set of data. In a box plot, we draw a box from the first quartile to the third quartile.

Box Plot

​​The five-number summary:

Min: Minimum or lowest number in the data set
Max: Maximum or highest number in the data set
Median: The value in the middle of the data set when the numbers are in order from least to greatest
Lower Quartile: The median of the lower half of the data when the numbers are in order
Upper Quartile: The median of the upper half of the data when the numbers are in order

Box and Whisker Plot

• The median is the value separating the first half of the data from the second half of the data.

• To find the median, you either find the middle most number, or take the two closest number to the middle, add them and divide by 2.

Box and Whisker Plot

• A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile.

Multiple Choice

What is the median of the data represented by the box plot?

• 65

• 12.5

• 20

• 143.75

Multiple Choice

What is the median of this data?

{12, 15, 18, 20, 23, 24, 40, 45}

• 20

• 23

• 22

• 15

• 20.5

Multiple Choice

What percentage of the data is contained between Q1 and Q3?

• 25%
• 75%
• 100%
• 10%
• 50%

Match

Match the following using the box plot example:

• Minimum

• Q1

• Median

• Q3

• Maximum

3

6

10

12

20

• 3

• 6

• 10

• 12

• 20

Match

Based on the box plot example, match the following:

• Minimum

• Q1

• Median

• Q3

• Maximum

5

10

17

20

32

• 5

• 10

• 17

• 20

• 32

​Construct your own data displays as directed using the data we collect as a group. You will use your scratch paper to do this.