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AS Applied Maths > Statistics 1 > Flashcards

Statistics 1 Flashcards

1
Q

Define population

A

Whole set of items of interest

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2
Q

Define census

A

Observation/measure of every member of the population

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3
Q

Name of the sampling units used for sampling from census?

A

Parameters

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4
Q

Define sample

A

Selection of observation from a subset of population in order to discover information about the population in its entirety

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5
Q

Name of sampling units used for sampling from sample?

A

Statistics

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6
Q

Advantage of a census?

A

-Completely accurate result obtained ( ie. everyone’s views recorded), giving true measure of population.

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7
Q

Disadvantages of a census?

A

-Time-consuming, labour-intensive and expensive
-Hard to contact whole population if applicable.
-Not used when testing involves the destruction of the item
-Hard to process large quantity of data

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8
Q

Advantages of a sample?

A

-Less-time consuming, labour-intensive and expensive
-If applicable, more easy to contact whole population
-Fewer people required to respond
-Less data to be processed

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9
Q

Disadvantages of a sample

A

-Data could be inaccurate
-Sample could not be large enough to inform of whole population by small sub-groups used

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10
Q

Correlation between a sample size and the validity of conclusions of the processed data.

A

Larger size of sample usually increases the validity of the conclusions of the processed data.

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11
Q

Unless using non-random sampling, requirement of sample?

A

To be random.

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12
Q

What does the size of a sample depend on.

A

-Accuracy required
-Resources available

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13
Q

Why is larger sample typically more accurate.

A

Larger proportion of data examined, more likely to be representative of population.

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14
Q

If population is very varied (heterogeneous)?

A

Size of sample required would be larger than that of a uniform (homogeneous) population.

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15
Q

Different samples can…

A

Lead to different conclusions due to the natural variation of a population.

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16
Q

Define sampling units.

A

The individual units of a population available for sampling.

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17
Q

Define sampling frame.

A

Where sampling units are individually named/numbered to form a list.

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18
Q

Criteria (generally) for representative sampling?

A

-Usage of random sampling method
-Typically, large sample size.

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19
Q

What is a biased sample?

A

One that does not accurately reflect the population, and perhaps favours a proportion of population over another.

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20
Q

How can you assess if a sample could be biased?

A

-Sample excludes people (based on age/gender/different interests (sweet sample outside of sweet shop) or habits (sport sampling at a sports centre) etc.)
-Sometimes, a small sample is likely to be biased.

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21
Q

If a sample is biased, what then can occur?

A

A sample unrepresentative of a population can lead in a sampling error.

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22
Q

Conclusion of data, on whole/average =x. Use data to agree/disagree with statement.

Steps

A

-Mean of data?
-Median of data?
-Presence of anomalies?
-Thus, mean/median better
(mean affected, median not)
-Hence, validity of data…

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23
Q

Define random sampling.

A

Where every member of the population has an equal chance of being selected for sampling (each sampling unit chosen by chance for sampling).

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24
Q

Thus, the sample performed under the methods of random sampling should be…

A

More representative of the population.

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25
Q

Benefit of random sampling as a whole.

A

It helps to eradicate the bias from sampling.

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26
Q

What are the 3 types of random sampling.

A

-Simple random
-Systematic
-Stratified

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27
Q

Discuss the method undergone of simple random sampling.

A

-Requirement of sampling frame.
-Utilisation of random number function of calculator or “lottery sampling”.
-Lottery sampling is where the members of the sampling frame are placed in a hat/other appropriate item, and then the required number of “tickets” are drawn from this object.

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28
Q

What are the advantages of simple random sampling.

A

-No bias
-Easy and cheap for small populations and small samples
-Each sampling unit has known and equal chance of selection

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29
Q

Disadvantages of simple random sampling.

A

-Not suitable with large population/sample size
-Requirement of a sampling frame.
-Only random if sampling frame is random.

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30
Q

Discuss the method undergone in systematic sampling.

A

-Required elements chosen at regular intervals from sampling frame.
-Regular intervals decided by number of units/required sampling size (n + x, n + 2x etc.)
-1st person chosen should be of randomised (1-x), then from then on the succeeding units are chosen at regular intervals (n+x, n+2x etc.) from the sampling frame.

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31
Q

Describe the advantages of systematic sampling.

A

-Simple and quick
-Suitable for large populations and sample sizes.

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32
Q

Describe the disadvantages of systematic sampling.

A

-Requirement of sampling frame
-If the 1st person chosen is not randomised, bias can be introduced into the sampling.
-Only random if sampling frame random

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33
Q

Possible limitation of systematic sampling?

A

Patterns could randomly occur in the selected data you have, not representative of all sub-groups of population.

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34
Q

Discuss the method undergone to perform stratified sampling.

A

-Population divided into mutually exclusive strata and random sampling occurs from each strata.
-The PROPORTION of each strata should be equal

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35
Q

What is the equation that decides what the number of strata will be to ensure its proportion of the overall population is equal to the rest.

A

No. of sample in the strata+ no of strata/no. of overall population x overall sampling size

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36
Q

What are the advantages of stratified sampling.

A

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

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37
Q

What are the disadvantages of stratified sampling.

A

-Population required to be classified into distinct strata.
-Selection process within each strata is not suitable for large population/ sample sizes
-Requirement of sampling frame.
-Only random if sampling frame random

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38
Q

Chance of being selected in a stratified sample.

A

-Assumed that each member has equal chance of being selected due to system of random sampling.

Then:
chance= number of groups selected x 1/number of groups of study.

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39
Q

What are the 2 types of non-random sampling.

A

-Quota sampling
-Opportunity/Convenience sampling.

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40
Q

Describe quota sampling.

A

-Interviewer/researcher selects a sample to try to reflect the characteristics of a population.
-Population divided into groups according to the given characteristic, with the size of each group determining the proportion of the sample that will have that specific characteristic.
-Interviewer meets people, assesses group, and subsequently allocates them into the appropriate quota
-This continues until all the quota are filled.

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41
Q

What occurs if a person refuses to be interviewed/person fits into quota already filled?

A

Simply ignored and researcher/interviewer moves onto next person.

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42
Q

What are the advantages of quota sampling.

A

-Allows a small sample to still be representative of the population so field work can be done quickly.
-Not requiring a sampling frame.
-Quick, administration easy, inexpensive.
-Allows for easy comparison between the different groups of a population.

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43
Q

What are the disadvantages of quota sampling.

A

-Methods of non-random sampling, with judgement of interviewer, can introduce bias
-Population must be divided into groups, which can be costly or inaccurate.
-Increase scope of the study increases the number of groups, hence increasing the time and expense.
-Non-responses are recorded as such.
-Not possible to estimate sampling errors
(due to lack of randomness)
-Difficulties of defining controls e.g. social class

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44
Q

What is the method of opportunity sampling.

A

-Taking the sample from people available at the time (e.g first n people saw etc.) of sampling who fit the criteria that is being researched.

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45
Q

Advantages of opportunity sampling.

A

-Easy to carry out
-Inexpensive.

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46
Q

Disadvantages of opportunity sampling.

A

-Unlikely that the sampling is representative of the population
-Is highly dependent on the individual researcher

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47
Q

How can non-random sampling data be made to be more representative.

A

Contextual to the question, try and make less biased and more representative. Thus, usually increasing size of sample size valid, and also, 1 way of eradicating bias (prevent exclusion of certain people etc.)

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48
Q

What is qualitative data/variables.

A

Variables/data associated with non-numerical (ie. categorical) observations, being descriptive.

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49
Q

Quantitative?

A

Variables/data associated with numerical observations, being numerical.

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50
Q

What is a continuous variable.

A

A variable that can take any value of a given range, data “measured”

51
Q

What is a discrete variable.

A

-Variable that can only take specific values in a given range, data “counted”.

52
Q

What is sometimes helpful to be done for large data?

A

To display it in frequency tables/as grouped data.

53
Q

Discuss the features of a grouped frequency table.

A

-Specific data values not shown
-Groups called classes
-Class boundaries are the maximum and minimum values that belong to each class
-Midpoint= Average of class boundaries.
-Class width= Upper class boundary- lower class boundary (difference of both)

54
Q

Why is data usually grouped?

A

For the purpose of comparison.

55
Q

If asked to compare 2 groups of data, 2 things looked at?

A

-Averages - mean usually, perhaps if anomalous median, if appropriate mode.
-General spread (skewness) of data- therefore would mean/median be more useful etc.

56
Q

What are the 5 UK weather stations.

A

-Camborne
-Hurn
-Heathrow
-Leeming
-Leuchars

57
Q

What are the coastal weather stations.

A

-Camborne
-Hurn
-Leuchars

58
Q

What are the inland weather stations.

A

-Heathrow
-Leeming

59
Q

What is the westernmost UK weather station.

A

Camborne.

60
Q

What is the northernmost UK weather station?

A

Leuchars

61
Q

What is the southernmost UK weather station?

A

Camborne

62
Q

What is the easternmost UK weather station?

A

Heathrow

63
Q

What UK weather station is the closest to the Isle of Wight.

A

Hurn

64
Q

What is the 2nd most northernmost weather station.

A

Leeming.

65
Q

What is the only non-English (Scottish) weather station.

A

Leuchars.

66
Q

What are the 2 international weather stations.

A

-Jacksonville, USA
-Beijing, China
-Perth, Australia.

67
Q

What are the coastal international weather stations.

A

-Jacksonville
-Perth

68
Q

What is the inland international weather station.

A

-Beijing

69
Q

What is the northernmost international station?

A

Beijing

70
Q

What is the southernmost (overall + international) weather station.

A

Perth

71
Q

What is the westernmost (overall +international) weather station.

A

Jacksonville

72
Q

What is the easternmost (overall + international) weather station.

A

Perth

73
Q

What is the northernmost overall weather station.

A

Leuchars

74
Q

What is the only weather station of the Southern Hemisphere.

A

Perth

75
Q

What is the daily mean temperature.

A

Average of hourly readings of temperature in a 24-hour period.

76
Q

Where is the temperature recorded.

A

1.25m from ground level, by thermometers with a lowered screen above short grass.

77
Q

What is the units of daily mean temperature.

A

Degrees celscius

78
Q

When is the daily mean temperature recorded.

A

0900 to 0900 GMT.

79
Q

What is the daily mean temp range for the UK weather stations?

A

Camborne: 10-20
Heathrow 8-29
Hurn: 6-24
Leeming: 4-23
Leuchars: 4-19

80
Q

What is the daily mean temp. range for the international weather stations?

A

Beijing 8-33
Jacksonville 15-31
Peth 8-25

81
Q

What is daily total rainfall measured in.

A

mm

82
Q

What, as well as rain are measured? How are they made recordable?

A

-Solid precipitation like hail/snow
-They are melted before being measured.

83
Q

What are amounts less than 0.05mm recorded as.

A

Tr (trace)

84
Q

How should trace values be written numerically in calculations using them?

A

0

85
Q

When is daily total rainfall measured.

A

0900 to 0900 GMT.

86
Q

What is daily total sunshine.

A

-Amount of solar radiation that exceeds a threshold.

87
Q

What are they recorded in.

A

Neatest tenth of an hour.

88
Q

What is daily mean wind direction recorded in.

A

Knots (nautical mph)
1 knot=1.15 mph

89
Q

When is daily mean wind direction recorded.

A

Average of data recorded between 0000 to 0000 GMT

90
Q

How are wind directions (meaned) recorded.

A

-As bearings/cardinal (compass) direction, rounded to the nearest 10 degrees.

91
Q

How is the daily mean windspeed recorded according to.

A

The Beaufort scale.

92
Q

How is daily mean windspeed measured.

A

A visiometer.

93
Q

Where is daily mean windspeed recorded from.

A

Averaged data recorded from 10m above ground level.

94
Q

What is the scale and term for windspeed less than 1km.

A

Scale=0
Term=Calm

95
Q

What is the scale and term for windspeed of 1-10km.

A

Scale=1-3
Term= Light

96
Q

What is the scale and term for windspeed of 11-16km.

A

Scale= 4
Term= Moderate

97
Q

What is the scale and term for windspeeds of 17-21km.

A

Scale=5
Term=Fresh

98
Q

What are the ONLY measurements conducted by international weather stations.

A

-Daily mean temperature
-Daily total rainfall
-Daily mean windspeed

99
Q

What is daily maximum gust.

A

-Highest instantaneous windspeed recorded.
-Direction from which the maximum gust blows is also recorded.

100
Q

What is the units of daily maximum gust.

A

Km

101
Q

What is daily maximum relative humidity.

A

How close air is to becoming saturated by water vapour

-Official term= percentage of air saturation that is water vapour.

102
Q

What are causative of relative maximum humidities of more than 95%?

A

Foggy/misty conditions.

103
Q

How is daily mean cloud cover measured.

A

Oktas= eighths of sky covered by cloud.

104
Q

What is the daily mean visibility.

A

Greatest horizontal distance at which an object can be seen in daylight.

105
Q

What would be the nightly mean visibility hence.

A

Greatest horizontal distance at which an object could be seen in the GENERAL ILLUMINATION OF DAYLIGHT.

106
Q

What is daily mean visibility measured in.

A

Decametres

107
Q

How is daily mean pressure recorded.

A

Hectopascals.

108
Q

How is daily mean pressure recorded.

A

Pressure at station level of the sea.

109
Q

When was data recorded from the specific weather stations to create the large data set.

A

-May-October 1987
-May-October 2015

110
Q

How are missing values indicated.

A

N/a (not available)

111
Q

Typical tendency of coastal locations.

A

Increased wind.

112
Q

Typical tendency of northern locations.

A

Decreased temperature

113
Q

Wettest city of 2015?

A

Jacksonville

114
Q

Windiest month of 2015?

A

May

115
Q

Wettest UK city of 2015?

A

Camborne

116
Q

Warmest UK location on average of 2015?

A

Heathrow

117
Q

Wettest month of 2015?

A

August

118
Q

Importance of 1987.

A

-Great Storm occurred
-On midnight of 15-16 October.

119
Q

Importance of 2015.

A

-Heathrow Airport affected by heavy rains of 26 August

120
Q

Temperature of international weather stations in ascending order of 2015.

A

-Jacksonville (coldest)
-Beijing
-Perth

121
Q

2015 importance for UK?

A

30 June, temperatures above 30 degrees celsius recorded.

122
Q

Importance for knowledge on place of measurements.

A

-Consistency
-Comparison

123
Q

Type of data collection that the Large Data Set is.

A

Secondary

124
Q

Importance of Heathrow geographically in terms of windspeed.

A

Windspeeds tendency to be high due to is affect of arrivals and departures in its airport.

AS Applied Maths (2 decks)

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