Statistics

Question 1

discrete vs continuous data

Answer 1

discrete:
- set number of values, eg shoe size

continuous:
- can have any value, eg height

Question 2

definition:

population

Answer 2

total set of possible values that could be selected for the sample

Question 3

definition

sampling unit

Answer 3

a single member of the population

Question 4

definition

sample

Answer 4

a selection of sampling units observed to make conclusions about population as a whole

Question 5

definition

sampling frame

Answer 5

a list of all members of the population

Question 6

advantages and disadvantages:

sample

Answer 6

advantages
- less time consuming/ expensive
- fewer people to respond
- less data to process than census

disavantages:
* data may not as accurate as census
* may not be large enough to give info abt small sub groups of population

Question 7

dis/advantages

census

Answer 7

pros
* should give accurate results

cons
* time / expensive
* can’t be used when testing process destroys the item
* hard to process large quantity of data

Question 8

Systematic sampling definition

Answer 8

A sample is formed by choosing members of a population at regular intervals using a list

Question 9

stratified sampling

Answer 9

• population divided into specific groups & random sample taken from e/ group
• proportion chosen from group equal to proportion sample size n is of total population N

Question 10

pros and cons of stratified sampling

Answer 10

PROS
* useful when very diff groups in population
* sample represenative of population structure
* members selected randomly

CONS
* can’t be used if not possible to split population into specific groups
* same cons as simple random

Question 11

opportunity sampling

Answer 11

sample is formed using available members of population who fit criteria

Question 12

Pros and cons of opportunity sampling

Answer 12

PROS
* Quick and easy
* useful when list of population not possible

CONS
* unlikely to be representative of population structure
* likely to produce biased results

Question 13

pros and cons of quota sampling

Answer 13

PROS
* useful when sampling frame not available
* sample will be representative of population structure
CONS
* may introduce bias as some members of the population may choose not to be sampled

Question 14

in a data set

outliers are

Answer 14

any data points 2 standard deviations more or less than mean

Question 15

in a box plot

outliers are

Answer 15

any data point that is 1.5x IQR more or less than upper or lower quartile

Question 16

how to work out estimated mean in a frequency table

Answer 16

• mid interval value (x)
• frequency (f)
• Efx / f

Question 17

coding

measure of location is affected by:
measure of spread is affected by:

Answer 17

measure of location is affected by: all operations
measure of spread is affected by: only multiplication or division

Question 18

linear interpolation

what do you do to the value when finding quartiles / percentiles for discrete data?

Answer 18

• decimal number: round up
• whole number: take average of x and next number

Question 19

How to work out outliers?

Answer 19

if not in the range:
[Q1-1.5(IQR)] , [Q3+1.5(IQR)]

Question 20

2 events CANNOT be both:

Answer 20

independent and mutually exclusive

because
- when mutually exclusive: P(A n B) = 0
- when independent: P(A n B) = P(A) x P(B) and these 2 cannot be equal

Question 21

to work out P(A l B’):

Answer 21

P(A n B’) / P(B’)

Question 22

probability

condition for independency:

Answer 22

P(AnB) = P(A) x P(B)

Question 23

condition for mutually exclusive:

Answer 23

P (A n B) = 0

Question 24

What is a histogram?

Answer 24

• A histogram: for grouped continuous data whereas a bar chart: discrete or qualitative data
• no gaps betw
• Whilst in a bar chart the frequency is read from the height of the bar, in a histogram the height of the bar is the frequency density
• On a histogram frequency density is plotted on the y– axis. This allows a histogram to be plotted for unequal class intervals
• It is particularly useful if data is spread out at either or both ends
• The area of each bar on a histogram will be proportional to the frequency in that class

Question 25

give a reason to justify the use of a histogram to represent these data

Answer 25

it is (unequal) grouped
continuous data
grouped frequency table given

Question 26

explain why using mean and standard deviation are just estimates

Answer 26

because the data is grouped so no exact values

Question 27

definition

census

Answer 27

observation of every member of a population to make a conclusion

Question 28

Write down the underlying feature associated with each of the bars in a histogram.

Answer 28

area of the bar is proportinal to the frequency

Question 29

Explain why a linear model may be appropriate to describe the relationship between f and d (positive correlation) (1)

Answer 29

point lie reasonably close to a straight line

Question 30

Reliability of extra data points using line of best fit (2)

Answer 30

• reliable: interpolation as …. within range of values collected
• unreliable: extrapolation as …. outside range of data collected