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Chapter 1 AP Statistics Notes

• Quantitative Data consists of numerical values. For instance, height or class size.

• Categorical Value consists of categories or group labels. For instance, eye color or marital status 

• Sample: 

• Population: 

Describing a Distribution 

• Context: Variable being measured

• Shape: Skew, modes, symmetric

• Outlier

• Center: Mean, median 

• Spread: Range, IQR, SD 

What’s an outlier? 

• An outlier is data that falls outside of the normal pattern of the group 

  • Ex. 77, 75. 78, 79, 5

    • In this dataset, 5 is the outlier. 

Mean  

Mean is the average in a dataset, and is calculated by dividing the sum of all the numbers in a data set by the number of values. 

Formula:

1. Practice problems: 

   1. What is the mean of: 77, 13, 61, 10

      1. 40.25 

   
   

Median (M)

The median M is the midpoint of distribution. In order to find the median of a dataset, you must arrange all data from least to greatest. If n, the number of values in a dataset, is odd, the median M is the center observation in the ordered list. If n, the number of values in a dataset  is even, the median M is the mean of the two numbers in the center 

1. Ex. 5, 1, 3, 4 , 10

   1. Arrange the numbers least to greatest: 1, 3, 4, 5 , 10

   2. In this case, there’s five different numbers so ODD. The numbers in the middle is 4. So Median is 4. 

2. Ex. 5, 1, 3, 4 ,

   1. Arrange the numbers least to greatest: 1, 3, 4, 5 

      1. In this case, there’s four different numbers so EVEN. The numbers in the middle are 3 and 4 so (3+4)/2 is 3.5 

Five-Number Summary

• The Five Number Summary gives the minimum number, first quartile, the median, the third quartile, and the maximum. 

  • Minimum - Q1 - M - Q3 - Maximum 

Interquartile Range

• Formula - IQR = Q3 - Q1

Standard Deviation 

• The Standard Deviation is to measure the DISPERSION of a SET of values

Chapter 2 AP Statistics Notes

Normal Distributions: 

• A normal distribution is symmetric around its mean value and adheres to the 68-95-99.7 Rule  

68-95-99.7 Rule

• σ (standard deviation): 68% of the observations fall within σ of the mean

• 2σ:  95% of the observations fall within 2σ of the mean

• 3σ: 99.7% of the observations fall within 3σ of the mean  

Practice Problem 

• The scores on a university examination are Normally distributed with a mean of 62 and a standard deviation of 11. If the bottom 5% of students will fail the course, what is the lowest mark that a student can have and still be awarded a passing grade?

1. Z = -1.65 

2. -1.65 = (x-62)/11

3. x=43.85 rounded up is 44

   1. ON THE CALCULATOR (TI-84 Plus)

      1. 2nd Vars

      2. invNorm()

         1. Area: 0.05

         2. Mean: 62

         3. Standard Deviation: 11

      3. Around 44