Center Shape and Spread of Data

Histograms

Unit 6 - Statistics

Math I Honors

Mr. Johnson

Learning Objectives

• Distinguish between histograms and bar charts 

• Interpret histograms and determine information from them

• Assess histograms for shape, center, and spread

• Develop a histogram using technology 

Histograms are NOT Bar Charts!

Histograms can only be used to represent QUANTITATIVE data. Bar charts are only good for representing QUALITATIVE data.

Interpreting Histograms

• ALWAYS look at the labels first!

• Frequencies

• "Bin" widths

• Frequency Density: multiply by bin width

Multiple Choice

• 63

• 56

• 53

• 43

Shape of Histograms

Skew is easy to see in a histogram!

Multiple Choice

How would you describe this distribution?

• Left skewed

• Uniform

• Right Skewed

• Symmetrical

Multiple Choice

Describe the histogram:

• Left Skewed

• Normal/Symmetrical

• Right Skewed

• Uniform/Flat

Center of Histograms

• Look for peak in your histogram!

• Symmetric: peak corresponds to median AND mean

• Skew: peak corresponds to median, less to mean

Multiple Choice

Which statement is true about the center of distribution?

• The center is best described using the mean, because the distribution is skewed.

• The center is best described using the median, because the distribution is skewed.

• The center is best described by the mean and median, because the distribution is symmetric.

• The center is best described by the outlier, because the distribution is symmetric.

Spread of Histograms

• Range = max - min

• Standard Deviation - COMPLEX formula, but technology can calculate it for us!

• The higher the SD, the greater the spread

Multiple Choice

What is the range of ages shown in this histogram?

• 10 years

• 30 years

• 20 years

• none of the above

Creating Histograms in Desmos

I will now demonstrate how to make histograms in Desmos. Afterward, we'll make a histogram from one of our class data sets and use it to answer questions.

Multiple Choice

Based on our class data histogram, what appears to be the approximate median hours of screen time?

• 0-2 hours

• 4-6 hours

• 6-8 hours

• 16-18 hours

Multiple Choice

Which best describes the shape of this histogram?

• Left skewed

• Symmetric

• Right Skewed

Exit Ticket

Check your understanding of this lesson's concepts!

Multiple Choice

If Raul measured another tree in the orchard, which is most likely the height of the tree?

• 12 feet
• 21 feet
• 3 feet
• 19 feet

Multiple Choice

How many students have more than 1,000 songs on their MP3 player?

• 5
• 16
• 10
• 4

Multiple Choice

Which interval has 400 employees?

• 33-43

• 0-10

• 77-87

• 66-76

Dropdown

When the majority of the data is distributed equally across the graph and there are no outliers, the graph is ​​

Select answer

u. Therefore the mean is ​

Select answer

the median.