AS EDEXCEL statistics unit 1

CHAPTER 1

• Mathmaticals models simplify real life issues
• Quick and easy to produce, improves understanding of the real world, enables predictions
• Only give a partial description, only work for a certain range of values
• Quantitative- describe data numerically
• Qualitative- describe non numerically
• Discrete- Can only be certain numbers/categories
• Continuous-Can be of any Value

CHAPTER 2

• Grouped data consists of classes and their class frequencies
• +/- 0.5 onto class boundaries if there is a gap between the classes
• modal class has highest frequency
• median is middle value when the data is ordered, for discrete data work out by dividing n by 2.
• For continuous grouped data use interpolation
• INTERPOLATION: Find median value by dividing n by 2.
  • Work out the fraction that median value is through that class
  • times by the class width
  • Add on lower boundary  eg   25.5+ 0.5x(30.5-25.5)
  •                                                                12
• MEAN: sum of x            OR       Sum of frequencies x mid point
•                    n                                         sum of the frequencies
• Use coding to simplify, then reverse any action taken to get the correct answer

CHAPTER 3

• Lower quartile is the 25th percentile for discrete data divide n by 4. For continuous grouped, use INTERPOLATION
• Upper quartile is the 75th percentile, for discrete data divide n by 4 then times by 3. For continuous grouped data use INTERPOLATION
• IQ range = UQ-LQ
• VARIANCE **see formula sheet

• STANDARD DEVIATION: square root of variance, **see formula sheet

• Coding for standard deviation and variance doesn't change anything.

• Multiplying or dividing does, so when you get a value via coding, do the reverse operation to it.

CHAPTER 4

• Stem and leaft diagram can be used to display data, must include a key. To compare two sets of data a back-to-back stem and leaf diagram can be used
• A box plot represents important features of a set of data
  • quartiles
  • maximum and minimum
  • Outliers
• If data is grouped continuous, then a histogram can be used to represent data. The height of the bar is frequency density, the area is frequency, and the width is the class width.
• FREQUENCY DENSITY: worked out using a formula ** see formula sheet.
• Skewness of data described using:
  • quartiles
  • shape of box plot
  • meaasures of location
  • FORMULA ** see formula sheet

CHAPTER 5

• P(A U B) everything in the circles of the venn diagram, A, B or both
• P(A n B) events A and B (intersection)
• P(A') Everything that isnt event A
• Complementary probability: P(A')= 1- P(A)
• Addition rule: P(A U B) = (P(A) + P(B)) - P(A n B)
• Conditional probability: P (A given that it is in B) = P(AlB) = P(A n B)
•                                                                                                               P(B)
• Multiplication Rule: P(A n B) = P(AlB) x P(B) OR P(BlA) x P(A)
• Independant if: P(A n B) = P(A) x P(B)
• Mutualy exclusive if: P(A n B) = 0