IB MATHS AI SL- Keywords for Sampling and Data

data

information about the characteristics of a group of individuals

categorical variable

describers a particular characteristic which can be divided into categories

quantitative variable

describes a characteristic which has a numerical value that can be counted or measured

population

an entire collection of individuals about which we want to draw conclusions

cenus

the collection of information from the WHOLE population

parameter

a numerical quantity measuring some aspect of a population

sample

a group of individuals selected from a population

survey

a collection of information from a sample

statistic

a quantity calculated from data gathered from a sample usually used to estimate a population parameter

four categories of error

sampling error, measurement error, coverage error and non-response error

sampling error

occurs when a characteristic of a sample differs from the whole population

- random

- occurs even for samples well chosen

measurement error

refers to inaccuracies in measurements at the data collection stage

coverage error

occur when a sample does not truly reflect the population we are trying to find information about

to avoid, samples should be large and unbiased

non-response error

occur when a large number of people selected for a survey choose not to respond to it

sampling methods

- simple random sampling

- systematic sampling

- convenience sampling

- stratified sampling

- quota sampling

simple random sampling

every member of the population has an equal probability of being selected for the sample

systematic sampling

select some starting point and then select every (n)th element in the population

convience sampling

create a sample by using data from population members that are readily available

stratified sampling

a variation of random sampling; the population is divided into subgroups and weighted based on demographic characteristics of the national population

quota sampling

a nonprobability sampling method in which elements are selected to ensure that the sample represents certain characteristics in proportion to their prevalence in the population

e.g y 11 has 100 people

y 12 has 200 people

so y12 has double the sample size

categorical variables

described a particular quality or characteristic

the data is divided into categories and the information collected is called categorical data e.g gender for male and female

quantitative variable

numerical values, information collected is called numerical data. they can be discrete or continuous

discrete quantitative variable (discrete variable)

takes the exact number values and it is usually a result of counting e.g apples on a tree

continuous quantitative variable (continuous variable)

takes any numerical value within a certain range and it is usually a result of measuring e.g times take to run a 100m race

tally

used to count the number of 1s 2s 3s and so on using 5 strokes to represent a group

frequency

summarises the number of occurrences of each particular data value

relative frequency

of data value is the frequency divided by the total number of recorded values. indicated the proportion of results which take that value

symmetric distribution

a distribution in which the data values are uniformly distributed about the mean, the mode is the highest point

negatively skewed distributuon

negative side is stretched (right)

outliers

data values that are either much larger or much smaller than the general body of data; they should be included in analysis unless they are the result of human or other known error

mode

1. the value that occurs most frequently in a given set of data.

positively skewed distribution

positive side is stretched (left)