Maths statistics

What is a census?

observes or measures every member of the population

Census advantages and disadvantages

• Add: very reliable

• Diss: hard or impossible to carry out

Sample advantages and disadvantages

• Add: easy to carry out

• Diss: not as reliable

What are the random sampling methods?

• simple random sampling

• systematic sampling

• stratified sampling

What is the method for simple random sampling?

• Number all items in the population

• Use random numbers to select sample

What is the method for systematic sampling?

• Number all items in the population

• Let 𝑛=𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑠𝑖𝑧𝑒𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑖𝑧𝑒

• Use random numbers from 1 to 𝑛 to select the first item

• Choose every 𝑛th item after that

What is the stratified sampling method?

• The population will be divided into groups.

• Decide how many to sample from each group using: 𝑛𝑢𝑚𝑏𝑒𝑟 𝑖𝑛 𝑔𝑟𝑜𝑢𝑝/𝑛𝑢𝑚𝑏𝑒𝑟 𝑖𝑛 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 ×𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑖𝑧𝑒

• Use simple random sampling to select the items from each group.

What are the non random sampling methods?

• Opportunity sampling (convenience Sampling)

• Quota sampling

What is the Opportunity sampling (convenience Sampling) method?

Your sample consists of any items which are available to be sampled.

What is the quota sampling method?

• The population is divided into groups. The same proportion of items from each group are included in the sample

• Opportunity sampling is used to sample items until the required number from each group has been sampled

What 2 time periods does the LDS cover?

• May to October 1987

• May to October 2015

When is the correlation negative and when id the correlation positive?

• When it tends to 1 it is positive

• when it tends to -1 it is negative

• 0 is no correlation

How to find the regression line pmcc ( r ) using a calculator?

• Select statistics mode ‘Menu 6’

• Select 2: 𝑦=𝑎+𝑏𝑥

• Enter data

• Then press ‘OPTN’ and select ‘4: Regression Calc’

• Calculator displays 𝑎 and 𝑏 for regression line in the form ‘𝑦=𝑎 +𝑏𝑥’ and ‘𝑟’ the pmcc

What to always start hypothesis testing in correlation with?

• 𝐻0: 𝜌=0

• 𝐻1: 𝜌<0 𝑜𝑟 𝜌> 0

steps to hypothesis testing with correlation

• Hypotheses

• Critical Region

• Compare

• Conclusion

Equation for mean

𝑀𝑒𝑎𝑛=∑𝑥 / n

Equation for median in non- grouped data

(n + 1) / 2

Equation for median grouped data

n / 2

Name examples of the measures of spread

• range

• lower quartile

• upper quartile

• interquartile range

How to use a calculator to be able to calculate mean, standard deviation, variance, median and the quartiles?

• MENU 6 (Statistics)

• 1 (1-Variable)

• Enter the data using =

• AC then OPTN

• 2 (1-Variable Calc

Define discreate data

Data which can be counted and has finite values

Define continuous data

Data which can take any value and is measured

What is the mean affected by in coded data?

• addition and subtraction

• multiplication and division

What is the standard deviation affected by in code?

just multiplication and division

What equation do you need to know for histograms?

FREQUENCY DENSITY = 𝐅𝐑𝐄𝐐𝐔𝐄𝐍𝐂𝐘 / 𝐂𝐋𝐀𝐒𝐒 𝐖𝐈𝐃𝐓𝐇

What number do you use in cumulative frequency?

the upper bound

What shape should a cumulative frequency graph be?

an S shaped curve

What is the area in a histogram proportional to?

the frequency

What units will standard deviation have?

the same units as the data

How do you model binomial distribution?

You can model a random variable 𝑿 with a binomial distribution 𝑩(𝒏,𝒑)

What are the 4 conditions for it to be binomial distribution?

• there are a fixed number of trials, 𝒏,

• there are two possible outcomes: ‘success’ and ‘failure’,

• there is a fixed probability of success, 𝒑

• the trials are independent of each other

How to use your calculator to find probabilities in binomial distribution?

• MENU (7) DISTRIBUTION

• For = probabilities (4) Binomial PD P-Probability

• For ≤ probabilities (↓1) Binomial CD C-Cumulative

• Then (2) Variable

• Enter your data using (=)

Draw A’ U B’

Draw A’ N B’

Draw (A U B)’

Draw (A N B)’

Draw A N B’

Draw A’ N B

What is true for statistically independent events?

𝑷(𝑨∩𝑩)=𝑷(𝑨)×𝑷(𝑩)

What is true for mutually exclusive events?

𝑷(𝑨∩𝑩)=𝟎 𝑎𝑛𝑑 𝑷(𝑨∪𝑩)=𝑷(𝑨)+𝑷(𝑩)

What is a mutually exclusive event?

When events have no outcomes in common

What is a statistically independent event?

When one event has no effect on another

What does 𝑷(𝑩|𝑨) mean?

the probability that 𝐵 occurs GIVEN that 𝐴 has already occurred.

𝑷(𝑩|𝑨)=

𝑷(𝑨 N B) / 𝑷(𝑩)

discrete / UNIFORM distribution

How is normal distribution displayed.

X~N(mew,varience)

What does mew in standard deviation represent?

the mean

What percentage of the data is within 1 standard deviation of the mean?

68%

What percentage of the data is within 2 standard deviations of the mean?

95%

What percentage of the data is within 3 standard deviations of the mean?

99.7%

What does Z in normal distribution mean?

its the standard normal

What is the mean and variance of the standard normal

mean= 0

variance= 1