Statistics Year 1

Front 1

What is the population?

Back 1

The whole set of items that are of interest

Front 2

What is a census?

Back 2

A sample that observes or measures every member of a population.

Front 3

What is a sample?

Back 3

A selection of observations taken from a subset of the population which is used to find out information about the population as a whole.

Front 4

What are the pros of a census?

Back 4

Give a completely accurate result.

Front 5

What are the cons of a census?

Back 5

Time consuming and expensive, hard to process large quantities of data. Cannot be used if the testing process destroys the item.

Front 6

What are the pros of a sample?

Back 6

Less time consuming and expensive. Fewer people need to respond. Less data to process.

Front 7

What are the cons of a sample?

Back 7

May not be as accurate. Sample may not be large enough to give information about small sub groups.

Front 8

What are the three types of random sampling?

Back 8

Simple random, systematic, stratified.

Front 9

Why is random sampling good?

Back 9

Random sampling helps to remove bias.

Front 10

What is a simple random sample?

Back 10

Every sample has an equal chance of being selected.

Front 11

How do you carry out a simple random sample?

Back 11

Each person is allocated a unique number and a selection of these numbers is chosen at random. Either by generating random numbers or lottery sampling (drawn from a hat)

Front 12

What is systematic sampling?

Back 12

The required elements are chosen at regular intervals from an ordered list.

Front 13

How do you take a systematic sample?

Back 13

For a sample size,n, from a population of size, P. You would sample every (p/n)th person. The first person to be sampled would be chosen at random from a number less than or equal to p/n.

Front 14

What is stratified sampling?

Back 14

The population is divided into mutually exclusive strata and a random sample taken from each.

Front 15

What should the sizes of each strata be?

Back 15

The proportion of each strata in the sample should be the same as the proportion of each strata in the population.

Front 16

What are the pros of simple random sampling?

Back 16

Free of bias, easy and cheap for small samples and populations. Each sampling unit has a known and equal chance of selection.

Front 17

What are the cons of simple random sampling?

Back 17

Not suitable when the population size or the sample size is large as it becomes time consuming, disruptive and expensive. A sampling frame is needed.

Front 18

What are the pros of systematic sampling?

Back 18

Simple and quick to use, suitable for large populations and samples.

Front 19

What are the cons of systematic sampling?

Back 19

Sampling frame is needed. Can introduce bias if the sampling frame is not random.

Front 20

What are the pros of stratified sampling?

Back 20

Sample accurately reflects the population structure. Guarantees proportional representation of groups within a population.

Front 21

What are the cons of stratified sampling?

Back 21

Population must be clearly classified into distinct strata. Selection within each stratum suffers from the same disadvantages as simple random sampling.

Front 22

What are the types of non-random sampling?

Back 22

Quota sampling, Opportunity sampling.

Front 23

What is quota sampling?

Back 23

An interviewer selects a sample that reflects the characteristics of the whole population.

Front 24

How do you take a quota sample?

Back 24

The population is divided into groups. The size of each group determines the proportion of the sample that should have that characteristic. As an interviewer you would meet people asses their group and then after the interview allocate them into the appropriate quota. This continues until all quotas have been filled.

Front 25

What is opportunity sampling?

Back 25

Taking the sample from people who are available at the time the study is carried out and fit the criteria.

Front 26

How do you take an opportunity sample?

Back 26

This could be the first 20 people you meet outside a supermarket on a Monday morning who are carrying shopping bags.

Front 27

What are the pros of Quota sampling?

Back 27

Allows a small sample to still be representative of the population. No sampling frame required. Quick, easy and inexpensive. Allows for easy comparison between different groups within a population.

Front 28

What are the cons of quota sampling?

Back 28

Can introduce bias. Population must be divided into groups which can be inaccurate. Large studies need lots of groups. Non-responses are not recorded.

Front 29

What are the pros of opportunity sampling?

Back 29

Easy to carry out, inexpensive.

Front 30

What are the cons of opportunity sampling?

Back 30

Unlikely to provide a representative sample. Highly dependent on researcher.

Front 31

What is a sampling frame?

Back 31

A list containing the sampling units of a population which are all individually named and numbered.

Front 32

What is a sampling unit?

Back 32

The individual units of a population.

Front 33

What is quantitative data?

Back 33

Data associated with numerical observations e.g shoe size.

Front 34

What is qualitative data?

Back 34

Non numerical data e.g hair colour.

Front 35

What is continuous data?

Back 35

Data that can take any value e.g height.

Front 36

What is discrete data?

Back 36

Data that can only take specific values e.g shoe size.

Front 37

What unit is visibility?

Back 37

Decametres, DM.

Front 38

What unit is pressure?

Back 38

Hectopascals, hPa.

Front 39

What are missing data values labelled as?

Back 39

N/A

Front 40

What unit is daily mean temperature?

Back 40

Degrees Celsius, readings taken every hour.

Front 41

What amount of rainfall is considered trace?

Back 41

Less than 0.05mm, including snow and hail.

Front 42

What unit is windspeed?

Back 42

Knots, the direction is given as a bearing or compass direction.

Front 43

What unit is humidity?

Back 43

A percentage of air saturation with water vapour.

Front 44

What are the three averages?

Back 44

Mode, Median, Mean

Front 45

What is the mode?

Back 45

Most occurring value or class.

Front 46

What is the median?

Back 46

The middle value.

Front 47

How do you find the quartiles?

Back 47

Divide n by 4. If this is a whole number then the quartile is halfway between this point and the next one. If it isn’t, then round up.

Front 48

How do you find the quartiles for grouped data?

Back 48

Divide n by 4 then use linear interpolation.

Front 49

What do you assume when you interpolate?

Back 49

You assume that the data values are evenly distributed within each class.

Front 50

What do extreme values affect?

Back 50

They affect the range they do not affect the IQR.

Front 51

How do you estimate variance?

Back 51

By assuming that every data point lies in the middle of each class. You can use this to estimate the mean as well.

Front 52

How do you find the mean?

Back 52

Σx/n or Σxf/Σf

Front 53

How do you find variance?

Back 53

Σx²/n−(Σx/n)² or Σfx²/Σf−(Σfx/Σf)²

Front 54

What is affected by coding data?

Back 54

The standard deviation. range and IQR are only affected by b. The mean and quartiles are affected by a and b. y=(x-a)/b

Front 55

What is an outlier?

Back 55

An outlier is any value that is 1.5 IQR's away from the upper or lower quartiles.

Front 56

What is cleaning the data?

Back 56

The process of removing anomalies from the data set is known as cleaning the data.

Front 57

When drawing box plots do you include outliers?

Back 57

When drawing a box plot you do not include outliers in the range, they are marked separately with a cross.

Front 58

How do you find the range from a box plot?

Back 58

Using the outliers on the box plot as the range includes outliers but the range in a box plot doesn't.

Front 59

How do you draw a box plot?

Back 59

First find the outliers then calculate the range and IQR without the outliers.

Front 60

What do you comment on when comparing data?

Back 60

Comment on a measure of location and a measure of spread.

Front 61

What is bivariate data?

Back 61

Data which has pairs of values for two variables.

Front 62

What is the independent variable?

Back 62

The research changed this, plotted on x-axis.

Front 63

What is the dependent variable?

Back 63

The researcher measured this, plotted on the y-axis.

Front 64

What is a casual relationship?

Back 64

When a change in one variable causes a change in the other.

Front 65

What is a least squares regression line?

Back 65

The straight line that minimises the sum of the squares of the distances of each data point from the line.

Front 66

What is interpolation?

Back 66

Using the regression line to make predictions for values of the dependent variable.

Front 67

What is extrapolation?

Back 67

Using the regression line to make predictions outside of the range.

Front 68

What can you not use the regression line for?

Back 68

You can only make predictions about the dependent variable and only inside the range.

Front 69

What is an experiment?

Back 69

A repeatable process that gives rise to a number of outcomes.

Front 70

What is an event?

Back 70

A collection of one or more outcomes.

Front 71

What is a sample space?

Back 71

The set of all possible outcomes.

Front 72

What does A∩B mean?

Back 72

The intersection of A and B also called A and B, where they overlap on a Venn diagram.

Front 73

What does A∪B mean?

Back 73

The union of A and B also called A or B, the circle of A and B.

Front 74

What does A' mean?

Back 74

Compliment of A, also called not A. Everything that isn't in the circle of A.

Front 75

What does mutually exclusive mean?

Back 75

When events have no common outcomes. They do not overlap on a Venn diagram.

Front 76

How do you show that two events are mutually exclusive?

Back 76

P(A or B)=P(A) + P(B)

Front 77

What does independent mean?

Back 77

When one event has no effect on the other.

Front 78

How do you show that two events are independent?

Back 78

P(A and B)=P(A) X P(B)

Front 79

What is a random variable?

Back 79

Is a variable whose value depends on the outcome of a random event.

Front 80

What is a sample space?

Back 80

The range of values that a random variable can take.

Front 81

When can you use binomial distribution?

Back 81

Fixed number of trials, two possible outcomes, fixed probability of success, trails are independent of each other.

Front 82

How do you write a binomial distribution?

Back 82

X ~ B(n,p)

Front 83

What is P(X=r) equal to?

Back 83

(n Choose r) p^r (1-p)^(n-r)

Front 84

What is a discrete uniform distribution?

Back 84

When all of the probabilities are the same.

Front 85

What is a hypothesis?

Back 85

A statement made about the value of a population parameter.

Front 86

What is the test statistic?

Back 86

The statistic calculated from the sample and not the population.

Front 87

What is the null hypothesis?

Back 87

The hypothesis which you assume is true. H(0).

Front 88

What is the alternative hypothesis?

Back 88

It tells you about the parameter if the null hypothesis is shown to be wrong. It is what you are testing about the parameter.

Front 89

What is the critical region?

Back 89

The region which causes you to reject the null hypothesis , if the test statistic falls within it.

Front 90

What is the critical value?

Back 90

The first value inside the critical region.

Front 91

What is the actual significance level?

Back 91

The probability of incorrectly rejecting the null hypothesis. This can be found by finding the probability of the critical value.

Front 92

How do you layout a hypothesis test?

Back 92

First, define X and P. Write down the distribution. Write down the hypotheses. Assume the null hypothesis is true then write down the distribution. Find the probability and compare it to the significance level. Write the conclusion.

Front 93

What conclusion do you write?

Back 93

There is not enough evidence to reject H(0). OR Reject H(0) there is sufficient evidence that .....

Then show what that means in context.