Download AP Statistics 1.3 Describing Quantative Data With Numbers: Five

AP Statistics
1.3 Describing Quantative Data With Numbers:
Five Number Summary and Boxplots,
Measuring Spread-Standard Deviation, Choosing Measures of Center and Spread
The Five-Number Summary
The minimum & maximum values alone tell us little about the
Likewise, the median & quartiles tell us little about the
To get a quick summary of both center & spread, combine
Five-Number Summary of a distribution consists of:
1. The smallest
2. The
3. The
4. The
5. The largest
*** written in order from
Minimum
𝑸𝟏
M
𝑸𝟑
Maximum
to
***
Boxplots (Box-and-Whisker Plots)
The five-number summary divides the distribution roughly into
This leads to a new way to display
, the boxplot.
How to Make a Boxplot
1. Draw & label a
2. Draw a central box from
3. Note the
4. Extend lines (whiskers) from the box out to the
Example using the “Stuck in Traffic” data.
Activity: Technology Corner Page 61. Use calculators to make boxplots with data on page 53
Measuring Spread: The Standard Deviation
Standard deviation is the most common measure of spread that looks at
Example using the number of pets owned by a group of 9 children
1. Calculate the mean: 𝑥̅ =
2. Calculate each deviation:
deviation = observation – mean
3. Square each deviation.
4. Find the “average” squared deviation.
Calculate the sum of the squared deviations divided by (𝑛 − 1)…this is called variance.
5. Calculate the square root of the variance…this is the standard deviation.
AP Statistics
1.3 Describing Quantative Data With Numbers:
Five Number Summary and Boxplots,
Measuring Spread-Standard Deviation, Choosing Measures of Center and Spread
Standard Deviation (𝑺𝒙 ) measures the average
. It is calculated by finding an average
and then taking the square root. This squared average is
called the
.
(x1 - x ) 2 + (x 2 - x ) 2 + ...+ (x n - x ) 2
1
variance = s =
=
(x i - x ) 2
å
n -1
n -1
2
x
1
2
standard deviation = sx =
(x
x
)
å i
n -1
Choosing Measures of Center & Spread
We now have a choice between 2 descriptions for center & spread:
1. Mean &
2. Median &
The Median & IQR are usually better than the mean & standard deviation for
Use mean & standard deviation only for
NOTE: Numerical summaries
. ALWAYS PLOT YOUR DATA!
Assignment on Pages 71-74. Do Problems: 91, 93, 95, 97, 103, 105, & 107-110
Take Quiz 1.3 A
Review Chapter 1. Chapter 1 AP Statistics Practice Test on Pages 78-81.
Take Chapter 1 Test