sampling and representing data

Question 1

Define a population

Answer 1

Whole set of items that are of intrest to the study

Question 2

What is a census?

Answer 2

Study that observes or measures every member of a population

Question 3

What is a sample?

Answer 3

Selection of observations taken from a subset of the population to find out information about the population as a whole

Question 4

Advantages of a census?

Answer 4

Gives a completely accurate result/representation

Question 5

Disadvantages of a census?

Answer 5

Time consuming and expensive
Expensive to process and store so much data

Question 6

Advantages of a sample?

Answer 6

Less time consuming; far cheaper
Less data to process/store

Question 7

Disadvantages of a sample?

Answer 7

May not be large enough to enlighten on small subgroups
Not as accurate as a census

Question 8

How to execute a simple random sample?

Answer 8

Give each item in the sampling frame an identifying number.
Use a random number gen. then go back to the sampling frame and select the items that corresponding lot-drawn numbers

Question 9

Advantages of simple random sampling?

Answer 9

• Bias free
• Cheap and easy to do
• Each item has a calculable and equal chance of selection

Question 10

Disadvantages of simple random sampling?

Answer 10

• Unsuitable for large population sizes
• Sampling frame (list of entities) required

Question 11

How to carry out a systematic sample?

Answer 11

Required elements are selected at regular intervals in an ordered list.
Take every kth element where:
k = pop. size / samp. size

starting with random item between 1 and k

Question 12

Advantages of systematic sampling?

Answer 12

• Quick and simple
• Suitable for large populations/samples

Question 13

Downsides of systematic sampling?

Answer 13

• Sampling frame required
• Bias risk if sampling frame is not random

Question 14

How to execute a stratified sample?

Answer 14

Divide population into strata (groups) and carry out a simple random sample in each group.
Use the same proportion:
samp. size / pop. size
sampled from each strata.
Use with large samples where pop. naturally divides into subgroups

Question 15

Advantage of stratified sampling?

Answer 15

• Reflects pop. structure
• Guarantees proportional representation within population of given groups

Question 16

Disadvantages of stratified sampling?

Answer 16

• Pop. must be defined by clearly distinct strata
• Selection from each strata suffers same pitfalls as simple random sampling

Question 17

How to execute quota sampling?

Answer 17

Divide a pop. into groups according to a characteristic.
Quota of items in each group is set to try to emulate groups’ proportion in whole pop.
Interviewer selects the actual sampling units

Question 18

Advantages of quota sampling?

Answer 18

• Lets small sample still be representative of pop.
• No sampling frame needed
• Quick, easy, inexpensive
• Allows easy comparison between groups in a pop.

Question 19

Disadvantages of quota sampling?

Answer 19

• Risk of bias
• Pop must be divided into groups: costly of inaccurate
• Increased scope increases costs and time
• Non-responses are not recorded.

Question 20

How to run an opportunity/convenience sample?

Answer 20

Take sample of people who are available at the time and fit the build

Question 21

Advantages of an opportunity/convenience sample?

Answer 21

• Easy
• Cheap

Question 22

Disadvantages of an opportunity/convenience sample?

Answer 22

• Unlikely to provide a representative sample
• Highly dependant on individual researcher

Question 23

What is an outlier?

Answer 23

An extreme value, commonly defined as being 1.5 IQRs beyond the upper and lower quartiles

Question 24

What are the features of a box plot?

Answer 24

Question 25

How do you draw a cumulative frequency diagram?

Answer 25

Go down the table adding the frequency of the row underneath to the sum of the ones before it until the whole table is done. plot the upper bound of the independent variable against the cumulative frequency for each row and draw a smooth curve to join these.

Question 26

How do you use a cumulative frequency diagram?

Answer 26

you can quarter the cumulative frequency to find the IQR and quartiles, along with working out percentiles, by working out the desired percent of the population, drawing from this value on the y axis to the curve and drawing straight down to find its corresponding x value on the independent variable scale

Question 27

What can be represented on a histogram?

Answer 27

continuous data given in a group frequency table

Question 28

How do you calculate the height of each bar on a histogram?

Answer 28

Known as the frequency density, this is calculable using the formula: area of bar = k X frequency k = 1 id the easiest value to use as if k = 1, freq. density = freq / class width

Question 29

How do you form a frequency polygon?

Answer 29

Join the middle of the top of each bar in a histogram:

Question 30

How do you figure out how many elements satisfy a value range that crosses multiple boxes in a histogram?

Answer 30

Find how many boxes the interval spans. Separate into each individual box. For full boxes, the no. entities will just be the frequency for that column (or CW * FD). work out percentage of class width needed in specific box. find the same percentage of the area (frequency). repeat for required boxes in range and sum together.

Question 31

How do you find the height and width of boxes in histograms when diagram has been scaled up but data is same?

Answer 31

Find class width and area of a normal box and do the same for the same representative box of the blown up diagram. Find separate S.Fs for the area and width and just scale components according to geometry

Question 32

How can you compare datasets?

Answer 32

By using mean and standard deviation or using the median and IQR. if dataset contains extreme values, Median and IQR are more suitable comparisons