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Maths A Level > Collecting And Interpreting Data > Flashcards

Collecting And Interpreting Data Flashcards

1
Q

What is a population?

A

A population is the whole set of items that are of interest

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2
Q

What is a sample?

A

A sample is some subset of the population intended to represent the population

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3
Q

What is a sampling unit?

A

Each individual in the population that can be sampled is a sampling unit

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4
Q

What is a sampling frame?

A

Sampling units of a population can be individually named or numbered to form a list called the sampling frame

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5
Q

What is a census?

A

Data collected from every sampling unit is known as a census

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6
Q

What are the advantages and disadvantages of a census?

A

Advantage: It should give completely accurate results
Disadvantage: Time consuming, expensive, impossible if testing involves destruction, lots of data to process

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7
Q

What are the advantages and disadvantages of a sample?

A

Advantages: Quick, Cheap, Less data to process
Disadvantages: Inaccurate, Miss out small sub groups

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8
Q

How do you carry out simple random sampling?

A

Every sample has an equal chance of being picked.
In sampling frame, each item assigned identifying number and a random number generator or “lottery sampling” is used to pick specific sampling units

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9
Q

What are the advantages and disadvantages of simple random sampling?

A

Advantages: Unbiased, Easy, Cheap, Equal Chance of Selection
Disadvantages: Impossible with large population, Sampling Frame needed

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10
Q

How to carry out systematic sampling?

A

Required elements are chosen at regular intervals in ordered list. Every kth elements where
k = pop size///samp size
Starting at a random item between 1 and k

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11
Q

What are the advantages and disadvantages of systematic sampling?

A

Advantages: Simple, Quick, Can do large samples
Disadvantages: Sampling frame needed, Bias if frame is not random

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12
Q

How to carry out stratified sampling?

A

Population divided into groups (strata) and simple random sampling occurs within them. Same proportion sampled from each strata:
Samp size///Pop size
Used when sample is large and population naturally falls into groups

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13
Q

What are the advantages and disadvantages of stratified sampling?

A

Advantages: Reflects population structure, Proportional representation of strata in population
Disadvantages: Population must be in strata, Same disadvantages as simple random sampling

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14
Q

How to carry out quota sampling?

A

Divide population into groups according to characteristics of interest to reflect population proportion. Interviewer selects the sampling units

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15
Q

What are the advantages and disadvantages of quota sampling?

A

Advantages: Small sample represents population, No sampling frame, Quick, Easy, Cheap, Easy comparison
Disadvantages: Possible bias, Costly or inaccurate to make groups, More groups is more expense, Non-response not recorded

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16
Q

How to carry out opportunity sampling?

A

Sample taken from people who are available at the time, who meet criteria

17
Q

What are the advantages and disadvantages of opportunity sampling?

A

Advantages: Easy, Cheap
Disadvantages: Unlikely to be representative sample, Dependent on researcher (bias)

18
Q

What does x bar mean?

A

X bar is the mean of the values in the variable ‘x’

19
Q

What are measures of location? Examples?

A

Measures of location are single values which describe a position in a data set (Maximum, Minimum, Quartile, Percentile)

20
Q

What are the measures of central tendency? Examples?

A

Within the measures of location, you have the measures of central tendency which are to do with the where the centre of data is (Mean, Medium, Mode)

21
Q

What are the measures of spread? Examples?

A

There are measures of spread which are to do with how data is spread out (Range, IQR, Variance, Standard Variation)

22
Q

What is the equation for x bar?

A

X bar = Total of X/Number of X values

23
Q

What is the x bar for a frequency table?

A

X bar = (Frequency***X)///Frequency

24
Q

What is the equation for x bar of grouped frequency?

A

X bar = (Average Frequency***X)///Frequency

25
Q

What is the equation for standard deviation?

A

Standard Deviation = Sqrt(Sigma x2 - n*x bar 2///n-1)

26
Q

How do you calculate the median for a list and grouped data?

A

To find the median, use the equation
Number of Values///2
If decimal, round up, if whole, use halfway between this item and the one after

With grouped data, it is the same equation and then linear interpolation

27
Q

What is the method behind linear interpolation?

A

Divide the median by the interval in the group data it is in. Multiply the fraction by the group interval and add this to the lower bound

28
Q

What is the formula for the Lower and Upper Quartiles?

A

UQ = 3(N+1)///4 LQ = N+1///4

29
Q

What is a formula to find an outlier using the IQR?

A

Data which lies 1.5 *** IQR beyond the lower and upper quartiles

30
Q

What is the formula for an outlier using standard deviation?

A

Data which lies +- 2 *** standard deviation from the mean

31
Q

What is variance and standard variation?

A

Variance is a measure of the spread between numbers in a data set from the mean

32
Q

What is the formula for variance?

A

Variance = Sigma x2 - (n)(x bar)///n-1

33
Q

What is a causal relationship?

A

Two variables have a causal relationship if a change in one variable directly causes change in the other

34
Q

What is the relationship between extrapolating and reliability?

A

Extrapolating outside the range of data compromises reliability

35
Q

What is cluster sampling?

A

The population is divided into smaller groups known as clusters of which simple random sampling is used to pick an entire cluster rather than a sampling unit. The groups are not connected by a characteristic like in stratified sampling

36
Q

What are the advantages and disadvantages of cluster sampling?

A

Advantages: Simple manual process, Cheap, Quick, Allows for increasing sample size
Disadvantages: Less precise, Leads to over/underrepresentation causing bias, Does not represent population structure well

37
Q

What does it mean if a set of data has a negative, positive, and symmetrical skew?

A

A negative skew is where the mean lies before the median
A positive skew is where the median lies before the mean
A symmetrical skew Is when the mean and medium lie together

Maths A Level (8 decks)

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