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Level 3 Core Maths
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Terms in this set (60)
What is quantitive data?
Discrete (has exact values)
Continuous (data can take any value in a given range)
What is qualitative data?
Things that can only be described (not counted or measured) e.g. colour, likely/unlikely
What is primary data?
Data you have collected yourself
What is secondary data?
Comes from other sources e.g. the internet
Data can be collected via?
Observations
Interviews
Questionnaires
Experiments
Tests
Give an example of the independent (explanatory) variable?
The temperature
Give an example of the dependent (responsive) variable?
The number of ice creams sold
What is a spurious correlation?
Where there is little/no connection between two data sets
What is bias?
Leaning toward a favourite
What is a census?
It asks for all member of a population to give feedback + provides understanding of trends within whole population
What is sampling?
It takes only a portion of the population and is used to reduce expense and time
What is a random sample?
Every member of the population has same chance of being selected usually via use of random number generator/table or computer program
What are the conditions of random sampling?
Members or items are similar
What are the advantages of random sampling?
No bias
What are the disadvantages of random sampling?
Time-consuming
What is cluster sampling?
Used when there are obvious different groups within a population - random sampling than applied.
What are the conditions of cluster sampling?
Distinctive groups/types within a population
What are the advantages of cluster sampling?
Cheaper + able to show regional variations
What are the disadvantages of cluster sampling?
Not a true random sample - can be biased
What is stratified sampling?
Each layer of a population is represented in proportion to size of stratum - random sampling occurs within
What are the conditions of stratified sampling?
Members are similar with identifiable groups/layers
What are the advantages of stratified sampling?
Proportionally representative - can highlight trends in each layer
What are the disadvantages of stratified sampling?
Time-consuming
What is quota sampling?
Given number of members from sections are chosen by interviewer. Randomness not necessary
What are the conditions of quota sampling?
Identifiable groups necessary
What are the advantages of quota sampling?
Easy to capture for most sections
What are the disadvantages of quota sampling?
Subjective; not truly random; bias is likely
What are the advantages of using the mean?
All data items are used
What are the disadvantages of using the mean?
Distorted by extreme values
What are the advantages of using the mode?
Good for qualitative data, no calculations needed
What are the disadvantages of using the mode?
Could be unrepresentative is a value is only repeated a few times/if two or three modes occur
What are the advantages of the median?
Not affected by extreme values
What are the disadvantages of the median?
Limited mathematical influence as is stagnant
What are the advantages of the range?
Gives the largest spread of data
What are the disadvantages of the range?
Extreme values may not represent the majority picture of the data
What are the advantages of using the upper/lower quartiles?
Not affected by extreme values
What are the disadvantages of using the upper/lower quartiles?
Not all values are considered
What are the advantages of using the IQR?
Gives the spread for the middle 50% of data so reduces the effect of extremes
What are the disadvantages of using the IQR?
Ignores half the data
What is the standard deviation?
A mean distance from mean of data set - compares how different data sets are spread out
What does a lower standard deviation imply?
More consistency within the set
What are the advantages of stem-and-leaf diagrams?
Good for small data sets, useful for finding median. Back-to-back can compare two sets
What are the disadvantages of stem-and-leaf diagrams?
Time consuming and less clear for large data sets
What are the advantages of using box and whisker plots?
Shows range, IQR, media + extent of skew. Useful for comparing.
What are the disadvantages of box and whisker plots?
Other work is required before it can be constructed
What are the advantages of cumulative frequency graphs?
Useful it source of data is unsure/lost. Can give estimates of median and quartiles
What are the disadvantages of cumulative frequency graphs?
Only estimates can be achieved
What are the advantages of histograms?
Gives proportional representation of each class interval within distribution. Median and quartiles can be estimated
What are the disadvantages of histograms?
Only estimates can be achieved
Where £315 is rounded to the nearest pound, what is the interval error?
50p (upper pound: £315.50, lower bound: £314.50)
How do you find a percentage of a quantity?
Decimal x quantity e.g. 0.35 x 175
How do you find one quantity as a percentage of another
Divide the quantity by the other quantity e.g 200/800 x 100
How to compare two quantities (percentages)?
Example: A salary of £22,000 is increased by £660 and a salary of £48000 is increased by £1000, which is the biggest increase?
660/22000 x 100
1000/48000 x 100
How to increase percentages?
Example:
150 x 1.15 (increase by 15%)
How do you find the original value (percentages) ?
Examples: Value of an apartment increases by 12% to £125,000
New price = 112%
Original price = 125000/112 x 100
Example: A pair of jeans is priced at £59.50 after a 30% reduction, what was the original price?
100%-30% = 70%
New price (70%) = £59.50
Original price = 59.50/70 x 100
What is simple interest?
Calculated based on original investment amount so same amount of interest is earned each year
What is compound interest?
Interest is also earned on interest paid in previous years
What is the formula for simple interest?
A = p + prt
What is the formula for compound interest?
A = p x (1+ r) ^t
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