Seftion 7 - Probability And Statistics Flashcards
How can you find the probability of a something if all possible outcomes are equally likely
Number of ways for something to happen divided by the total number of possible outcomes
What does a sample space diagram do
Shows all the possible outcomes
Like a Punnett square
What’s the product rule
The number of ways to carry out a combination of activities equals the number of ways to carry out each activity multiples together
How do you work out relative frequency
Frequency divided by number of times you tried the experiment
Calculates estimate of probability for something biases
What happens to the accuracy when you do an experiment more times
The more times you do it, the more accurate your estimate of probability should be
What’s a frequency tree
You can record results - shows outcomes and then answers
How do you calculate expected frequency
Expected frequency of s result = probability X number of trials
Can estimate how many times you’d expect something to happen if you do it n times
The expected frequency is based on probability of the result happening
What’s an independent event
If one event happening doesn’t affect the probability of the other happening
What’s a dependant event
If one event happening does affect the probability of the other happening
The events are dependent
Tell me how to work out the probability of both events happening
If two events, call them a and b are independent then
P(a and b) = p(a) X p(b)
Tell m the formula for events a OR b happening
If events can happen together
P(a or b) = p(a) + p(b) - p(a and b)
What’s mutually exclusive
When two events can’t happen together
Tell me the formula for working out probability of event a or b happening when they can’t happen together
P(a or b) = p(a) + p(b)
What are the 4 key tree diagram facts
On any set of branches which meet at any point add to one
Multiply along the branches to get the end probabilities
Check your diagram - the end probabilities add to 1
To answer any question, add up relevant end probabilities
Tell me about “at least questions”
“At least, a certain number of things happening - easier to work out:
1 - probability of less than that number of things happening
Tell me about conditional probabilities
The conditional probability of a given b is the probability of event a happening given that event b happens
What’s the and rule for conditional probabilities
CONDITIONAL
P(a and b) = p(a) X p(b given a)
Tell me about conditional probabilities on tree diagrams
The probabilities on a set of branches will change depending on previous event
What’s a set in a Venn diagram
Collections of things - call things elements
Tell me about sets on Venn diagrams
Can be written in curly brackets
N(a) just means the number of elements in a set
In a Venn diagram each set is represented by a circle containing the elements of the set or the number of elements in the set
What’s a sample
A smaller group of the Desired population
Can apply those conclusions to whole populations
For a sample to be representative what must it be
A random sample - means every member of population has an equal chance of being in it
Big enough for size of population - bigger the sample the more reliable
How do you select a simple random sample
Assign a number to every member of populations
Create a list of random names
Match the random numbers to members of the population
Tell me the problems of a sample
A biased sample is one that doesn’t properly represent whole populations - to spot it think about: when, where and how it was taken,
How many members were in it
If certain groups excluded it’s not random and is biased
What’s primary data
Data you collect yourself
What’s secondary data
Data someone else has collected
What’s qualitative data
Different type of showing data
It’s descriptive and uses words and not numbers
What’s quantitative data
A way of showing data
Measures quantities using numbers
What’s discrete data
Can only be exact values
What’s continuous data
Data can be any value
How do record data into classes
Group data into classes - discrete should have gaps between eg 1-2 or 2-3
Continuous data should use inequalities to make classes
Make sure no classes overlap
What’s the mean
Total of items divided by number of items
What’s the mode
Most common value
What’s the median
The middle value when values placed in order of size
What’s range
Difference between highest and lowest values
What’s the golden rule for median
Always rearrange the data in ascending order for median
How do you calculate the mode in a frequency table
The mode is just the category with the most entries
How can range be calculated from a frequency table
Found from the extreme me of the first column
If a value has a 0 frequency use next value
How do you calculate median from a frequency table
The category containing the middle value
Work out position
How do you calculate the mean of a third column.
Add a 3rd Column multiplying first column X frequency
Add up values to find total then divide by the total of frequencies
3rd column total divided by 2nd column total
How do you find the mean from a grouped frequency table
Find the mid interval and multiply it by frequency and total it
Total of mid interval X frequency divided by the frequency
Tell me about box plot interquartile range
The difference between the upper quartile and lower quartile - contains 50% of values
Tell me what a box plot shows
Shows the minimum and maximum values in a data set and the values of quartiles
Doesn’t tell you induvidual data values - show range
What’s cumulative frequency
The total frequency so far, add each value and add and add to previous value
What does a histogram show
A bar chart with different widths
The vertical axis on a histogram is the frequency density
How do you calculate frequency density
frequency density = frequency divided by class with
frequency = area of bar (frequency density X class width )
What’s a time series
What you get if you measure same thing at different times
A basic pattern often repeats itself
Look at overall trend
What’s a moving average
Calculating different averages at different points and see how it changes
How do you find a 2 point moving average
Find the mean of 1st and 2nd values
Find mean of 2nd and 3rd
Find mean of 3rd and 4th
Until you reach the last pair
It shows the trend
