Chapter 1 -data collection

population

whole set of items that are of interest

raw data

info from population

census

measures every member of population

sample

a selection of observations from a subset of population to find out info of population as a whole

sampling units

individual units of population that are numbered to form a sampling frame

sampling frame

a list of all sampling units in a population

why might sampling frame differ to population

not always possible to keep this list up to date

adv of census

completely accurate results

disadv of census

time consuming; expensive; can’t be used when testing destroys process; hard to process large amounts of data

how does size of sample affect results

larger samples are better for large populations as they are more accurate but more resources are required

disadv of sampling

not as accurate as census; sample may not be large enough to give us info about small subsets

adv of sampling vs census

less time consuming; cheaper; less data processed

when is a census used

population known, small and easily accessed

when is sample used

population known, largest too time consuming and expensive to interview all

what are the 3 types of random sampling

simple, systematic and stratified

describe simple random sampling

each sample of size n is allocated a random number and then samples picked from a random number generator, so equal chance of getting selected

adv of simple random sampling

free of bias; easy and cheap to implement

disadv of simple random sampling

time consuming if large population; sampling frame needed

describe systematic sampling

First person is randomly selected and then required elements are chosen at regular intervals from an ordered list

adv of systematic random sampling

simple; quick; suitable for large populations

disadv of systematic sampling

sampling frame needed; can introduce bias if sampling frame is not random

describe stratified sampling

random samples are taken from mutually exclusive groups of the population. Sample sizes within strata are in strict proportion to numbers in each strata in the population

how to calculate the number sampled from each strata

strata size/population size x overall sample size

adv of stratified sampling

accurately reflects population structure and guarantees proportional representation of all groups; random sampling within strata reduces bias

disadv of stratified sampling

clearly classified strata needed; selection within each strata has same disadv as simple sampling

2 types of non random sampling

quota sampling and opportunity sampling

describe quota sampling

interviewer divides population into groups based on characteristics and selects a fixed number of individuals from each group to make up the sample

adv of quota sampling

small sample is representative of the whole population; quick easy and cheap; easy comparison between groups; no sampling frame needed

disadv of quota sampling

can introduce bias; population must be divided into groups which may be costly and inaccurate; varied population mens more groups which adds time and expense; non responses not recorded d

describe opportunity sampling

taking a sample of those available at the time of study and who fits the criteria looked for

adv of opportunity sampling

easy to carry out and inexpensive

disadv of opportunity sampling

not representative; dependant on researcher

quantitive data

data assosciated with numerical observations

qualitative

data associated with non-numerical observations

continuous data

can taken any value within a given ranged

discrete data

can only take specific values within a given range

months of large data set

May to oct

countries named south to north

Cambrone, Hurn, Heathrow, Leeming, Leuchars

which places are coastal + windy

Cambrone and Leuchars

trend ofr max no of sunshine

north has a higher max

range for mean temp

5-24

range for daily mean temp

0-20

what does tr mean

trace so number is between 0<r<0.05.

range for daily total sunshine

0-14 hours

what is cloud cover measured in

oktas

range for cloud cover

0-8 (integers)

humidity range

70-100% - integers

what is daily mean visibility measure in

Decametres (10m = 1Dm)

range for daily mean visibility

200-4000 (roundest to nearest 100)

daily mean pressure units

hPa

lowest and highest daily mean pressure

900 to 1040 hPa (integers)

units for daily mean windspeed

knots

range for daily mean windspeed

3 - 10 kn (integers)

windspeed (beaufort conversion)

light - moderated ; most days are light

max gust

8-50 knots (integers)

wind direction

10 - 360 degrees (multiples of 10; where wind is blowing from not to)

features of Jacksonville florida

hot summers

Perth features

flipped seasons

features of beijing

hotter but wetter summers, colder winters

equation for linear interpolation

lower boundary + (class width / frequency of class x (value - cumulative frequency up to class))

when should you use median and IQR instead of mean and standard deviation

When there are outliers as outliers affect the mean and standard deviation

explain how Charlie would use quota sampling to obtain a sample of 40 workers

ask 20 men and 20 women how long their journey was

effect on standard deviation by a translation of points

no effect as standard deviation is not affected by addition or subtraction as it is a measure of spread

how to clean data before standard deviation and mean calculations

replace tr with a numerical value. Trace values are between 0 and 0.05

Explain why daily total rainfall data from large data set would not be suitable to find annual mean daily total rainfall

data only covers may to oct so not representative of whole year. Winter months are missing and we would expect more rain in this season so an estimation from large data set would be an underestimation

explain why a binomial distribution B(14,0.27) to model the number of days without rain for a 14 day summer event would not be suitable

p=0.27 is unlikely to be constant and the probability in a binomial distribution should be constant

median of daily mean pressure

around 1000 hPa

range of daily mean pressure

50 hPa

state the assumption involved with using the midpoint to calculate an estimate of a mean from a grouped frequency table

assumes that data is distributed uniformly throughout the class

why does it not matter about using the midpoint with the large data set to calculate an estimate for the mean total daily rainfall

most of the data in the first class is 0

why is the median appropriate for this data set

it is not affected by an extreme outlier

Sara is investigating the variation in daily maximum gust in Camborne in June and July. She selected the first value randomly and the selected every third value after that. Explain why this process may not generate a sample size of 20

in the LDS, some days have gaps because data was not recorded

A random sample of 20 customers is taken. How does a scout group affect the validity of the model

The sample requires 20 customers to be random and the scout group may invalidated this so binomial distribution would not be valid

suggest two improvements to a pulley model

include a more accurate value of g, include the dimensions of the ball so the distance it falls changed,

suggest two limitations of the pulley model

the pulley may not be smooth, air resistance

describe something significant about rainfall in perth

lots of zeros for rainfall

in the refined model, the effect of air resistance is included. How would the new value for the speed to ball hits the ground vary

the new value would be lower

for overseas locations, what is the only data recorded

daily mean temp daily total ranfall, daily mean pressure, daily mean windspeed