# GCSE Statistics

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Population

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## Tags and Description

### 85 Terms

1

Population

A collection of all the items

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2

Sample

A selection of the population to use data from

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3

Census

When data is taken from every member in the population

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4

Advantages of a census over a sample

More representative, less biased, includes everyone's opinions

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5

Advantages of a sample over a census

Quicker, cheaper, easier to analyse as less data

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6

Disadvantages of a census over a sample

Time consuming, expensive, difficult to do

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7

Disadvantages of a sample over a census

Less representative, possibly biased

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8

Pilot Study

A small scale replica of the survey to be carried out.

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9

Ensures questions can be understood, identify ambiguity, test response rate, identifies likely responses, check methods

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10

Sampling Frame

A list containing data that a sample can be taken from

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11

Examples of a sampling frame

Electoral role, SIMS register, DVLA, telephone directory

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12

Primary Data

Data that has been collected by the person doing the survey

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13

Secondary data

Data that hasn't been collected by the person doing the survey

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14

More reliable, up-to-date, tailored for investigation

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15

Easier to obtain, cheaper, less time-consuming

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16

Continuous Data

Data that lies on a continuous scale (can be at any point on a number line)

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17

Discrete Data

Data that consists of separate numbers (jumps along the number line)

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18

Quantitative Data

Data that has numerical values

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19

Qualitative Data

Data that is not numerical values

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20

Open Questions

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21

Allows for a range of responses, so can cover all eventualities

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22

Closed Questions

Has a set of answers for the person to choose from

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23

Easier to analyse as range of responses restricted

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24

Questions that infer an opinion and promote a certain answer

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25

Convenience Sample

The first so many pieces of data in the list are sampled

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26

Quick and easy

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27

Unlikely to be representative

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28

Random Sample

Each person has an equally likely chance to be picked

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29

How to take a random sample

(a) Number everyone in list
(b) Use a random number generator to select numbers
(c) Select the data points corresponding to the numbers picked
(d) If you get a number outside the range or the same number twice you repeat, if you get a decimal round to the nearest number.

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30

Easy to do

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31

May not be representative

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32

Systematic Sample

Data is chosen at regular intervals (e.g. every 10th person)

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33

How to take a systematic sample

Order population and divide population by sample size to find how often data chosen. Then choose random number to decide where in this interval to start.

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34

Useful for production line - will spot problems over time

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35

May not be representative

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36

Quota Sample

The same amount of people from different chosen groups are sampled

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37

How to take a quota sample

Decide on a quota size for each group. Then take a random sample, ignoring any results from a group where the quota has been reached.

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38

Makes sure all quota groups are represented, easy to take

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39

Not likely to be representative, may be difficult to reach quota if numbers limited

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40

Cluster Sample

The population is divided into groups and a group is chosen at random.

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41

Easy to do

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42

Unlikely to be representative

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43

Stratified Sample

Where the data sampled in each group is proportional to that of the whole population

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44

How to take a stratified sample

Multiply the fraction of each group in the whole population by the total sample size to decide on the size of the sample in each strata. Then take a random sample.

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45

Representative

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46

Harder to collect, more expensive

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47

Features of a good question

Unambiguous, closed, non-overlapping answer boxes, unbiased/not leading, not offensive or personal, easy to analyse

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48

Positive correlation

As one variable increases, so does the other

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49

Negative correlation

As one variable increases, the other decreases

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50

Response variable

The variable being measured or studied

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51

What values does the SRCC lie between and what do they mean?

-1 and 1.
1 = Perfect positive correlation
0 = No correlation
-1 = Perfect negative correlation

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52

What does the symbol x with a line above it mean?

The mean average value of x

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53

How is frequency represented on histograms?

By area

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54

What do we call the height on a histogram?

The frequency density

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55

What does the capital sigma (that looks like an 'E') symbol mean?

Sum

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56

How is the IQR calculated?

UQ - LQ

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57

How much of the data is contained within each quartile?

25%

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58

How do define the median?

The middle value in a dataset

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59

How would we compare two distributions given their median and IQR?

Higher median = higher result on average
Higher IQR = less consistent on average

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60

How would I define outliers?

Low outliers < LQ - 1.5 x IQR
High outliers > UQ + 1.5 x IQR

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61

What does a positive skew look like?

The median is closer to the LQ than the UQ.

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62

What does a negative skew look like?

The median is closer to the UQ than the LQ.

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63

If a line of best fit is given by y = ax + b, what does 'a' mean?

For every unit the 'x' variable increases, the 'y' variable increases by 'a'.

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64

What does a normal distribution look like?

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65

How much of the data is within 2 s.d. of the mean for a normal distribution?

95%

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66

How much of the data is within 3 s.d. of the mean for a normal distribution?

99.8%

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67

What conditions need to be met for a binomial distribution?

Two outcomes (success or failure), fixed number of independent trials, fixed probability of success

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68

What is a discrete uniform distribution and what would it's graph look like?

The same probability for all events. The graph is a bar chart with each possible outcome going to the same height (the probability of it happening).

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69

How could one compare values from different sets of data?

Use a standardised score.

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70

How is a standardised score calculated?

(score-mean)/s.d.

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71

What is an index number?

A number that shows the rate of change in quantity, value or price of an item over a period of time.

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72

How is an index number calculated?

100*[(quantity in given year)/(quantity in base year)]

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73

What is a chain base index number?

The annual percentage change in quantity, value or price of an item. It is found by using the previous year as the base year.

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74

What is a trend line?

A line of best fit through moving averages

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75

How would you describe a trend line?

As increased or decreasing, not as positive or negative

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76

What is the average seasonal variation?

The mean average difference between the trend line and actual value for a given season

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77

How can one predict values using a trend line?

Read the value from the trend line for the season wanted and add/subtract the average seasonal variation

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78

Why might one not want to predict a value from a scatter graph or trend line?

If the correlation is not strong enough or if the prediction lies outside the range of data (extrapolation)

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79

Mutually Exclusive

Two events that cannot happen at the same time.

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80

Independent events

Two events that have no impact on one another (one happening doesn't affect the probability of the other)

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Exhaustive

A set of events that covers all possibilities

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82

What do the probabilities of mutually exclusive exhaustive events sum to?

1

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83

When they are mutually exclusive.

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84

When can we multiply probabilities?

When they are independent.

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85

What might we use to find probabilities of two events following one another?

A tree diagram.

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