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A Level Maths > stats > Flashcards

stats Flashcards

1
Q

what is a population?

A

the whole set of items that are of interest

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2
Q

what is a sample?

A

some subset of items chosen from the population

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3
Q

what is sampling unit?

A

each individual thing in the population that can be sampled

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4
Q

what is a sampling frame?

A

a numbered list of the entire population - individually named or numbered

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5
Q

what is a cenus?

A

data collected from an entire population

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6
Q

compare census and sample:

A

census:
✓gives a 100% accurate result
✖time consuming
✖expensive
✖cannot be used when testing involves destruction
✖large volume of data to process

sample:
✖data may not be large enough to represnt small sub-groups

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7
Q

how could you improve sample size

A

use a larger sample size

mention number (10% of population size)

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8
Q

what is a sampling error?

A

the difference between the actual value and the value to got from a sample

eg: comparing your sample results to the census results

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9
Q

What is bias?

A

the systematic error in the collection of the sample

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10
Q

what can result in a biased sample?

A
  • sample not representative of the population
  • leading questions- are you a law abiding citezen
  • the wrong person asking questions
  • small sample size
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11
Q

what is random sampling?

A

every item has an equal chance of being selected for sample

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12
Q

what is non-random sampling?

A

sample selection is based on other factors than just random chance

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13
Q

what is simple random sampling?

SRS

A

every sample has an equal chnace of being seleted

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14
Q

how would you carry out simple random sampling?

A
  • allocate a number between 1 ans N to each individual- so tht every item in sampling frame has an identifying number
  • using a random number generator to select ‘15’ different numbers between 1 and ‘120’ discard any repeated numbers or numbers above ‘120’, select 2 digit numbers at a time
  • **individulas corresponding to these numbers become the sample **
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15
Q

what are the advantages and disadvantages of simple random sampling?

A

✓bias free
✓cheap and eay to implement
✓each individual has a known equal chance of being selected
✖not suitable when population size is large
✖sampling frame needed

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16
Q

what is systematic sampling?

A

required elements are chosen at regular intervals in ordered list
(first perosn is also chosen at random)

the sampling frame must be random, there shpuld be no patterns

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17
Q

how would you carry out systematic sampling?

A
  1. determine k
  2. randomly select a number between 1-k
  3. start with the individulal of this number
  4. select the every kth person
  5. these people will be in the sample
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18
Q

what are the advantages and disadvantages of systematic sampling?

A

✓simple
✓suitable for large samples
✖sampling frame needed
✖can introduce bias if the sampling frame is not random

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19
Q

what is stratified sampling?

A

the population is dividied into groups (strata) and a simple random sample is carried out in each group
same proportion is taken from each group

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20
Q

how would you carry out stratified sampling?

A
  1. perform calculation to know how many you want from each group
  2. label each group from ‘1- 15’
  3. use random number generator to select ‘2’ different numbers from1-15
  4. those with the corresponfong numbers become the sample
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21
Q

what are the advantages and disadvantages of stratified sampling?

A

✓reflects population structure
✓gurantees proprtional respresentation of groups within population
✖population must be clearly classified into distinct strata
✖sampling frame needed

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22
Q

what is convenience sampling?

A

samples are taken from people who are available at time of study, who meet criteria

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23
Q

what are the advantages and disadvantages of opportunity sampling?

A

✓easy to carry out
✓inexpensive
✖unlikley to provide a respresentative sample, reflect the
✖highly dependant on individual reseracher

24
Q

what is cluster sampling ?

A

each cluster is defined (should be reprentative of population)
collect samples from each cluster

eg: taking samples from each grammar school

25
Q

what are the advantages and disadvanatges of cluster sampling?

A

✓no sampling frame ✓inexpensive
✖unlikley to provide a representative sample because cluster tend to have similar characteristics

26
Q

what is quota sampling?

A

population is divided into groups according to characteristic.
A quota of items are set to try and reflect the groups prprtion in the whole population
interviewer selects the actual sampling units

non random stratified sampling

27
Q

what are the advanatges and disadvantages of quota sampling?

A

✓sample is representative of population
✓no sampling frame required
✓easy/inexpensive
✓allows easy comparision between different groups in population
✖non random so can introduce bias
✖population must be divided into group s- cosyly or innacurate
✖non-responses are not recorded

28
Q

What are the different types of data?

A
29
Q

Which type of data is the following

A
30
Q

How do you conduct linear interpolation?

A
31
Q

How would you compare or describe a data set?

A

Measures of central tendency Describe the centre of data.
Measures of spread suggest how consistent the data is

32
Q

What would you consider an outlier (using IQR)?

A

Anything that is more than 1.5 × IQR

33
Q

What would you do when there at gaps between each interval

A
34
Q

What is the notation for mean?

A
35
Q

How do you calculate the mean on your calculator?

A
36
Q

Plot these values into the calculator to find mode mean and median

A

Because there are two columns, make sure you tell it that the frequency column is list 2

37
Q

what is self selected sampling?

A

people are asked wehather they want to take part

38
Q

what are the rpos and cons of self selected sampling?

A

cheap/ easy
biased results

39
Q

Find the standard deviation

A

Set the 1Var Frequency to List 2
Then calculate Var1

sx= (our exam board ) =5.02

40
Q

Calculate the mean

A
41
Q
A
42
Q

What is the position of the median?

A

(n+1) /2

43
Q

Why would median be used over the mean?

A

If there are more extreme values, you would not used the mean as they account for them.

44
Q

Which position would be used for the 57th percentile

A
45
Q

Find an estimate for the median

A
46
Q

How would you determine the “skew” of the data?

A

The side to which the least values are (the tail)

If mean > median: positively skewed
If mean < median: negatively skewed

47
Q
A
48
Q
A
49
Q

What are the two different formulas for standard deviation?

A

sx=

50
Q
A
51
Q

What is considered an outlier using standard deviation?

A

Any value more or less than 2 standard deviations from the mean
2(sx) + mean
Or mean -2(sx)

52
Q

What would be considered an outlier using the IQR?

A

IQR x 1.5 from UQ and LQ

53
Q

What does variance measure ?

A

The average degree to which each squared point differs from the mean

54
Q

What does standard deviation measure?

A

Looks at how spread out a group of numbers is from the mean

55
Q

What are some common mistakes when calculating standard deviation?

A

Using (Σx)^^2 instead of Σ(x)^^2
Using a rounded version of the mean which gives rounding errors

A Level Maths (25 decks)

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