Statistics

Question 1

What is the most important form of central tendency? (3)

Answer 1

• Standard deviation
• The bigger the standard deviation the bigger the dispersion of data
• Important for analysing the variability of ROI

Question 2

What is discrete data? (4)

Answer 2

• Data that cannot be split up / whole numbers
• Data can be categorised - ‘categorical data’ e.g. 1 for yes, 2 for no, 3 for maybe
• Sometimes this may be ranked and ordered ‘ordinal data’ e.g. first and second class degree
• Data can be descriptive - provide simple summaries about the samples and measures

Question 3

What is continuous data? (2)

Answer 3

• Units have constant scale and unlimited decimal places
• Level of accuracy depends on the precision of the measuring device itself

Question 4

What is a population? (2)

Answer 4

• Set of items which have desired characteristics
• Gives a complete set of data but can be time consuming to collect

Question 5

What is a random sample? (1)

Answer 5

• Every member of the population has an equal chance of being selected

Question 6

What is non-random sampling? (6)

Answer 6

• Quota sampling - often used in market research, quota is used to categorise different types of invidiual members e.g. first 100 people investigator meets in the city
• Stratified sampling - designed to reduce sampling error
• Systematic sampling - researchers select the nth record of a population e.g. asking every 5th person
• Convenience sampling - choosing a sample that is the easiest to collect information form
• Judgement sampling - making a judgement of the sample that would best represent the population
• Snowball - relies of referrals of initial subjects

Question 7

How is continuous data presented? (4)

Answer 7

• Time series graphs
• Histograms
• Semi-log graphs
• Scatter graphs

Question 8

How is discrete data presented? (2)

Answer 8

• Pie charts
• Bar charts

Question 9

What are the 3 central tendencies and what are their measures of dispersion? (3)

Answer 9

• Mean - standard deviation
• Median - Interquartile range (upper quarter minus the lower quarter)
• Mode - Range

Question 10

What is the mean? (3)

Answer 10

• Standard deviation
• Simple arithmetic mean
• x = sum of X / n

Question 11

What is the problem with standard deviation?

Answer 11

• Does not capture the entire population and may miss extreme values

Question 12

What is the problem with mode and range? (3)

Answer 12

• There may be more than one mode - bi-modal, tri-modal
• May be no mode at all
• Range can be distorted by extreme values

Question 13

What are the assumptions of a normal distribution curve? (6)

Answer 13

• Mean, median and mode all have the same value
• 50% of observations fall on either side of the curve
• Approx 68.26% of observations willl be within 1 standard deviation either side of the mean
• Approx 95.5% will be 2 standards deviations either side of the mean
• Approx 99.75% will be 3 standards deviations either side of the mean
• When extreme conditions occur, the normal distribution will have ‘fat tails’

Question 14

What are the assumptions of skewed distribution curves? (2)

Answer 14

• If the peak curve is on the left of the centre, it is positively skewed. Mean, median and mode are not in alphabetical order
• If the peak curve in on the right of the centre, it is negatively skewed. Mean, median and mode are in alphabetical order

Question 15

What is geometric mean? (2)

Answer 15

• The average rate of change over a given period
• Particularly useful when looking at compound changes such as changes in share prices or portfolio returns

Question 16

What is covariance? (4)

Answer 16

• The statistical measure of the relationship between two variables, e.g. two share prices
• If the variables move in the same direction, positive covariance relationship
• If the variables move in the opposite direction, negative covariance relationship
• If the variables are moving independently of each other, the covariance is zero

Question 17

What is correlation? (8)

Answer 17

• Correlation coefficient measures the strength of the relationship between two variables, such as two share prices
• -1 = perfectly negative
• 1 = perfectly positive
• 0 = uncorrelated
• Positive correlation = increase in one variable increases with another
• Negative correlation = increase in one variable decreases with another
• Perfect correlation = changes in both variables are directly proportional
• Autocorrelation = can be used to predict the future of an asset
• Correlation does not imply causation - just because two variables are moving in the same direction, doesn’t mean one is causing the other to move - this could be influence by a third party and market conditions e.g war

Question 18

How do you calculate standard deviation?

Question 19

How do you calculate bivariate linear regression?

Question 20

How do you calculate the geometric mean?