Seftion 7 - Probability And Statistics

Question 1

How can you find the probability of a something if all possible outcomes are equally likely

Answer 1

Number of ways for something to happen divided by the total number of possible outcomes

Question 2

What does a sample space diagram do

Answer 2

Shows all the possible outcomes

Like a Punnett square

Question 3

What’s the product rule

Answer 3

The number of ways to carry out a combination of activities equals the number of ways to carry out each activity multiples together

Question 4

How do you work out relative frequency

Answer 4

Frequency divided by number of times you tried the experiment

Calculates estimate of probability for something biases

Question 5

What happens to the accuracy when you do an experiment more times

Answer 5

The more times you do it, the more accurate your estimate of probability should be

Question 6

What’s a frequency tree

Answer 6

You can record results - shows outcomes and then answers

Question 7

How do you calculate expected frequency

Answer 7

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

Question 8

What’s an independent event

Answer 8

If one event happening doesn’t affect the probability of the other happening

Question 9

What’s a dependant event

Answer 9

If one event happening does affect the probability of the other happening

The events are dependent

Question 10

Tell me how to work out the probability of both events happening

Answer 10

If two events, call them a and b are independent then

P(a and b) = p(a) X p(b)

Question 11

Tell m the formula for events a OR b happening

If events can happen together

Answer 11

P(a or b) = p(a) + p(b) - p(a and b)

Question 12

What’s mutually exclusive

Answer 12

When two events can’t happen together

Question 13

Tell me the formula for working out probability of event a or b happening when they can’t happen together

Answer 13

P(a or b) = p(a) + p(b)

Question 14

What are the 4 key tree diagram facts

Answer 14

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

Question 15

Tell me about “at least questions”

Answer 15

“At least, a certain number of things happening - easier to work out:

1 - probability of less than that number of things happening

Question 16

Tell me about conditional probabilities

Answer 16

The conditional probability of a given b is the probability of event a happening given that event b happens

Question 17

What’s the and rule for conditional probabilities

CONDITIONAL

Answer 17

P(a and b) = p(a) X p(b given a)

Question 18

Tell me about conditional probabilities on tree diagrams

Answer 18

The probabilities on a set of branches will change depending on previous event

Question 19

What’s a set in a Venn diagram

Answer 19

Collections of things - call things elements

Question 20

Tell me about sets on Venn diagrams

Answer 20

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

Question 21

What’s a sample

Answer 21

A smaller group of the Desired population

Can apply those conclusions to whole populations

Question 22

For a sample to be representative what must it be

Answer 22

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

Question 23

How do you select a simple random sample

Answer 23

Assign a number to every member of populations

Create a list of random names

Match the random numbers to members of the population

Question 24

Tell me the problems of a sample

Answer 24

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

Question 25

What’s primary data

Answer 25

Data you collect yourself

Question 26

What’s secondary data

Answer 26

Data someone else has collected

Question 27

What’s qualitative data

Answer 27

Different type of showing data

It’s descriptive and uses words and not numbers

Question 28

What’s quantitative data

Answer 28

A way of showing data

Measures quantities using numbers

Question 29

What’s discrete data

Answer 29

Can only be exact values

Question 30

What’s continuous data

Answer 30

Data can be any value

Question 31

How do record data into classes

Answer 31

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

Question 32

What’s the mean

Answer 32

Total of items divided by number of items

Question 33

What’s the mode

Answer 33

Most common value

Question 34

What’s the median

Answer 34

The middle value when values placed in order of size

Question 35

What’s range

Answer 35

Difference between highest and lowest values

Question 36

What’s the golden rule for median

Answer 36

Always rearrange the data in ascending order for median

Question 37

How do you calculate the mode in a frequency table

Answer 37

The mode is just the category with the most entries

Question 38

How can range be calculated from a frequency table

Answer 38

Found from the extreme me of the first column

If a value has a 0 frequency use next value

Question 39

How do you calculate median from a frequency table

Answer 39

The category containing the middle value

Work out position

Question 40

How do you calculate the mean of a third column.

Answer 40

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

Question 41

How do you find the mean from a grouped frequency table

Answer 41

Find the mid interval and multiply it by frequency and total it

Total of mid interval X frequency divided by the frequency

Question 42

Tell me about box plot interquartile range

Answer 42

The difference between the upper quartile and lower quartile - contains 50% of values

Question 43

Tell me what a box plot shows

Answer 43

Shows the minimum and maximum values in a data set and the values of quartiles

Doesn’t tell you induvidual data values - show range

Question 44

What’s cumulative frequency

Answer 44

The total frequency so far, add each value and add and add to previous value

Question 45

What does a histogram show

Answer 45

A bar chart with different widths

The vertical axis on a histogram is the frequency density

Question 46

How do you calculate frequency density

Answer 46

frequency density = frequency divided by class with

frequency = area of bar (frequency density X class width )

Question 47

What’s a time series

Answer 47

What you get if you measure same thing at different times

A basic pattern often repeats itself

Look at overall trend

Question 48

What’s a moving average

Answer 48

Calculating different averages at different points and see how it changes

Question 49

How do you find a 2 point moving average

Answer 49

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