statistics

• primary data - collect yourself

  secondary data - collected by someone else
• discrete data - counted data

  continuous data - measured data
• quantitative - numerical

  qualitative - words
• census - entire population

  sample - part of population
• census

  advantage - limited/no bias

  disadvantage - time consuming,expensive and difficult to collect
• Sample

  advantage - cheaper,less time consuming easier

  disadvantage - could be biased
• simple random sampling - every member of the sample has an equal chance of being selected
• Non-random sampling where the sample selection is based on factors other than just random chance,in other words it is biased in nature
• Non random sampling types are - opportunity sampling,cluster sampling,quota sampling,systematic sampling,stratified sampling
• Cluster sampling

  The population is split into smaller groups called clusters. One or more clusters are chosen at random and the sample is everyone in those clusters
• Opportunity sampling advantages

  • Easy to do
  • Quick
  • Cheap
• Cluster sampling advantages

  • Representative of the population if clusters are representative of the population
  • Time and cost efficient
• Opportunity sampling disadvantage

  • Can be biased based on where you chose to stand/time of day
• Cluster sampling disadvantage

  • High sampling error
  • Complex
• Opportunity sampling

  A sampling type where you pick a location to stand and ask people at that location
• Quota sampling

  Where you select people of a certain type for your sample
• Systematic sampling

  The sample is chosen from the sample frame by picking randomly and choosing the rest of the sample at regular intervals
• Stratified sampling

  Each sample matches the proportion of the entire population
• Quota Advantages

  quick and easy

  cheap

  representative of target population
• Quota disadvantages

  large potential for bias

  Not generalisable to population
• Systematic advantages

  Easy to do

  Easy to use for a large population
• Systematic disadvantages

  Potential for bias
• How to conduct a random sample

  Number the population in a list

  Randomly select n members using a random number generator

  Ignore,repeats continue until you have n unique numbers
• When getting the midpoint of age from a table you have to add 0.5 to the midpoint
• For discrete data

  LQ=n+1/4

  Median=n+1/2

  UQ=3(n+1)/4
• For continuous

  LQ=n/4

  Median=n/2

  UQ=3n/4
• Cumulative frequency graph

  Plot the cumulative frequency against the END POINTS

  start from 0

  Join all points curve
• Histogram

  Frequency=frequency density x class width
• Box plots

  No skew median is in middle mode=median=mean

  Positive skew median closer to LQ mode<median<mean

  Negative skew meadian closer to UQ mode>median>mean
• When comparing data from box plots you need to comment on the median,the spread(IQR or range) and skewness and also add context
• Any number more than 1.5 IQR's away from the nearest quartile is an outlier

  You still need to include any outliers as x or .

  Anything more than 2 standard deviations away from the mean is also considered an outlier.
• Regression line

  In the form y=a+bx

  the co-efficient tells you the change in y for each unit change in x
• Mutually exclusive is two events that can't happen at the same time
• AUB

  Everything in A and B
• AnB

  The intersection of A and B
• A'

  Everything but A
• Discrete - typically integer value

  E.g shoe size,number of students
• Continuous - typically fractions or d.p

  E.g foot length,height,weight,time,temperature,age
• Binomial Distribution is used when:

  An experiment is repeated a given number of times

  When there are only 2 outcomes (fail/success)

  The trials are independent from each other,so the probability of success is the same each time
• Binomial PD if (X=5)

  Binomial CD if (X<or equal to 5)