Analyzing Box and Whisker Plots, Histogram and Data Distribution

Analyzing Histogram and Data Distribution

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What a Box and Whisker Plot look like?

Get it!!!

​Interpreting the box and whisker plots

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•Easily see lightest / heaviest and range

•The ‘box’ contains the middle 50% of people (the most ‘representative half’)

•The ‘whiskers’ show the lightest 25% and heaviest 25% of people (extremes)

​Comparing Groups 1

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1. ​​“Lightest girl lighter than lightest boy”

2. ​“Heaviest boy heavier than heaviest girl”

3. ​“Most representative half of girls generally lighter than most representative half of boys”

Multiple Choice

In which river are the lengths of the fish more variable?

• River B as the lower quartile is bigger

• River B because it has the minimum length

• River A because the upper quartile is bigger

• River A because the IQR is bigger

Multiple Choice

In which river are the lengths of the fish on average longer?

• River B as the median is bigger

• River B because the lower quartile is bigger

• River A because the upper quartile is bigger

• River A because the maximum value is bigger

Multiple Select

Which of these comparisons are correct?

• Boys weigh more than girls on average

• The lightest girl is lighter than the lightest boy

• The heaviest boy is the same weight as the heaviest girl

• Girls weight is less consistent than boys

​Comparing Groups 2

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1. ​​“Lightest girl same as lightest boy”

2. ​“Heaviest boy same as heaviest girl”

3. ​“All of the most representative half of girls lighter than most representative half of boys”

4. ​“Three quarters of girls lighter than three quarter of boys”

​Some Terminology

Symmetrical Distribution

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​Some Terminology

​Positive skew: median closer to Lower Quartile (Q1) than the Upper Quartile (Q3).

​Some Terminology

​Negative skew: median closer to Upper Quartile (Q3) than Lowere Quartile (Q1)

What does a Box and Whisker Plot includes?

Other Names:

Lower Extreme = Least Value = Minimum

Lower Quartile = First Quartile = Q1

Median = Q2

Upper Quartile = Third Quartile = Q3

Upper Extreme = Greatest Value = Maximum

Multiple Choice

Which is NOT in the middle 50% of data values?

• 17
• 15
• 21
• 11

Multiple Choice

If 44 values were used for the data, about how many data values are greater than the 1st quartile?

• 11
• 22
• 33
• 128

Multiple Choice

Which value is in the top 25% of the data?

• 16
• 22
• 29
• 36

Multiple Choice

True of false, 75% of the data values are greater than 18?

• True
• False, 75% of the values are greater than 16
• False, 50 % of the values are greater than 18
• False, 25% of the values are greater than 18

Multiple Choice

Find the median of plot B

• 30
• 14
• 28
• 16

Multiple Choice

What is the difference in the upper extremes of the two plots?

• 18
• 40
• 22
• 16

Multiple Choice

What is the interquartile range of plot A?

• 6
• 8
• 15
• 28

Multiple Choice

If plot B has 60 numbers in it, about how many are in the box?

• 15
• 30
• 60
• 120

Multiple Choice

Which has a Median of 1?

• Zach 
• Steven 
• They both have a median on 1

Multiple Choice

Which plot has a median of 50?

• Plot 1

• Plot 2

• Plot 3

• Plot 4

Example 2: Create A Histogram

Use the frequency table on The Golf Tournament Scores to create a histogram,

Histograms

-a bar graph used to display the frequency of data divided into equal intervals

-the bars must be of equal width and should always touch but never overlap

Multiple Choice

Which graph represents histogram?

Multiple Choice

According to the histogram, how many people are 10 or younger?

• 4

• 6

• 10

• 11

Multiple Choice

Identify the data set that represents the histogram.

• 1, 2, 3, 10, 11, 12, 13, 14, 15, 16, 17, 18

• 1, 10, 11, 13, 13, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18, 18, 18

• 2, 10, 11, 12, 12, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 18, 18

• 2, 11, 11, 12, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18, 18

Multiple Choice

What percent of cards sold were valued between $0.50 and $1.00?

• 4%
• 20%
• 25%
• 15%

Multiple Choice

How many cards were sold between $1.00 and $1.50?

• 4
• 7
• 3
• 6

Dot Plots

Each dot represents one answer. In the sheet to the right, 3 students answered that they had 0 cookies at lunch. 5 said they had 2 cookies.

Multiple Choice

This is a

• dot plot

• frequency table

• relative frequency table

• histogram

Multiple Choice

What is the spread of the data?

• 2

• 1

• 4

• 12

Multiple Choice

What is the mode of the data?

• 2

• 1

• 4

• 12

Multiple Choice

What is the median of the data?

• 2

• 1

• 3

• 12

Multiple Choice

This is an example of a

• dot plot

• frequency table

• relative frequency table

• histogram

Multiple Choice

This is an example of a

• histogram

• dot plot

• frequency table

• relative frequency table

Multiple Choice

This is an example of a

• histogram

• dot plot

• frequency table

• relative frequency table