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Transcript of Chapter 1.2
1.3 Measures Of Center
Mean - Ex: pg 50 - "non-resistant"
Median - Ex's: pg 53-54 - "resistant"
Mode - Duh....
Midrange - (H + L)/2
Measures Of Spread
Example - pg 62-63 How Many Pets?
Summary - pg 64
The Box Plot!!!
5 Number Summary - pg59
Min, Q1, Med, Q3, Max
Modified Box Plot - Plotting outliers
TALK ABOUT THE......
ShApE, cEnTeR, sPrEaD!!!!!!
Oh yea....and make comparisons IN CONTEXT of the problem!!!!!
Displaying Quantitative Data with Graphs
Dot Plots - AP Favorite!!
How to Examine the Distribution
Overall Pattern - Departures from the Pattern
Shape - Symmetric/Skewed (almost never perfectly symmetric..."approximately")
Center - "Middle" (Mean/Median)
Spread - How much variability? (St. Dev/Range/IQR)
Outlier - Differ from overall pattern
** pg 28 for S/C/SP/O help "SOCS" - Interpreting a Dot Plot
** pg 30 for Example on Shape - Don't worry about little ups and downs in a distribution, little irregularities are to be expected, nothing is PERFECT :-)
Using Histograms WISELY
Don't confuse histograms and bar graphs!
Don's use counts (in a FT) or percents (in a RFT)
Use percents instead of counts on the vertical axis when comparing distributions with different numbers of observations.
Just because it looks nice, doesn't mean it is meaningful!
** READ pg 39-41to DOUBLE CHECK!
Comparing the Mean and Median
Mean - "Average"
Median - "Typical"
Choosing Measures of Center and Spread
Who Texts More—Males or Females?
Pulling it all together
For their final project, a group of AP Statistics students investigated their belief that females text more than males. They asked a random sample of students from their school to record the number of text messages sent and received over a two-day period. Here are their data:
What conclusion should the students draw? Give appropriate evidence to support your answer.
STATE: Do the data give convincing evidence that females text more than males?
PLAN: We’ll begin by making side-by-side boxplots. Then we’ll calculate one-variable statistics. Finally, we’ll compare shape, center, spread, and outliers for the two distributions.
DO: Make a sketch of the boxplots we obtained from our calculator. The table below shows numerical summaries for males and females.
Median vs. Mean?
Shape: Both distributions are heavily right-skewed.
Center. On average, females text more than males.
The median number of texts for females (107) is about four times as high as for males (28). In fact, the median for the females is above the third quartile for the males. This indicates that over 75% of the males texted less than the “typical” (median) female.
Spread: There is much more variability in texting among the females than the males. The IQR for females (157) is about twice the IQR for males (77).
Outliers: There are two outliers in the male distribution: students who reported 213 and 214 texts in two days. The female distribution has no outliers.
CONCLUDE: The data from this survey project give very strong evidence to support the students’ belief that females text more than males. Females sent and received a median of 107 texts over the two-day period, which exceeded the number of texts reported by over 75% of the males.
What's your Mode?
Comparing Distributions - Ex: pg 32
Stem Plots - Ex: pg 33
Splitting Stems Fig1.14
Back-to-Back Fig 1.15
***DON'T FORGET KEY AND LABELS!!!!
Histograms - Ex: pg 35
Most common graph of quantitative variables.
Minimum 5 classes
BOUNDARIES!! - Use a dot plot to visualize and draw boundaries!!
Histogram Calc HELP!! - pg 38-39
Recommend Check your understanding here....
How to make a Dot Plot
AP EXAM TIP!!! pg 32
Relative Frequency Histograms - often more useful because sample size does not affect percents ;)
Shape/Center/Spread/Outliers - Revisited
pg 37 - READ IT
Pg 41 - CHECK YOUR UNDERSTANDING!!!
Making the graph is not the end all-be all, always ask yourself, "What do I see?"
AP EXAM COMMON ERROR!!
When asked to "compare distributions", SOCS!!!!
You will not receive full credit unless you address all 4 parts - Shape, Center, Spread, Outliers - and use phrases like "about the same as" and "much greater/less than".
Think of VARIABILITY - CONSISTENCY....
Range is not resistant due to outliers affecting min/max.
IQR is resistant, it ignores smallest and largest 25% of the values in a distribution!
pg 56 - Calculate Quartiles
Identify Outliers - pg 57
NEVER SAY NORMALLY DISTRIBUTED FOR BOX PLOT, just say "symmetric" - Box plots do not show modes!!