Lecture 4 REVISED

Question 1

continuous variable

Answer 1

can take on any value in an interval

e.g., worker’s hourly income can take on any value between 0 and infinity

Question 2

discrete variable

Answer 2

can only take on set, distinct values within in interval

e.g., how many people chose blue as their favourite colour can only be whole number values

Question 3

what levels of measurement are required for continuous variables?

Answer 3

interval or ratio

Question 4

rectangle in a histogram is called a…

Answer 4

bin

Question 5

how does a discrete/continuous data distribution look on a graph?

Answer 5

discrete: bars
continuous: curve

Question 6

frequency distribution is…

Answer 6

a tabular summary of a dataset showing the frequency of items in each class

Question 7

symmetric, skewness, kurtosis in frequency distributions?

Answer 7

symmetric: distribution is split into two identical halves

skewness: level of asymmetry in which an elongated tail extends

kurtosis: degree of peakedness/steepness in a distribution

Question 8

when a distribution is perfectly symmetrical, what is the relationship between the mean and median?

Answer 8

mean and median are the same values

when a distribution is skewed, this isn’t the case

Question 9

why does the median tend to be more representative than the mean?

Answer 9

because if a distribution isn’t symmetrical, an outlier may skew the mean/average

Question 10

where is the mode in a frequency distribution?

Answer 10

the peak

Question 11

what formula is used to find the position of the median value?

Answer 11

(n+1) / 2

Question 12

what is the formula to calculate standard deviation?

Answer 12

• subtract the mean from each value
• square all the deviations and add them together
• divide this by (n-1)
• square root this figure

Question 13

what does standard deviation tell us about the dataset?

Answer 13

how close each value is from the mean

small standard deviation = low amount of variability, values are close to the mean

high standard deviation = high variability, values are far from the mean

Question 14

variance relationship with standard deviation?

Answer 14

standard deviation is the square root of the variance

Question 15

density curve

Answer 15

an idealised description of a data distribution

describes the overall pattern of a distribution

Question 16

disadvantage of variance for practical applications?

Answer 16

its units differ from the units of the variable

hence why standard deviation is more commonly reported as a measure of dispersion

Question 17

if the dataset is a sample/population, how is the standard deviation denoted and calculated??

Answer 17

sample: denoted s, calculated by dividing the squared deviations by n-1

population: denoted sigma, calculated by dividing the squared deviations by n

Question 18

mean absolute deviation (MAD)

Answer 18

measures the absolute distance/deviation of values in a dataset from the mean

Question 19

how is MAD calculated in a sample/population?

Answer 19

divide the sum of the deviations by the number of data points

Question 20

what does MAD indicate?

Answer 20

how spread out data is

Question 21

percentile

Answer 21

describes the percentage of data values that fall at or below another data value

Question 22

how to calculate percentiles?

Answer 22

(p/100)n

percentile in question divided by 100 multiplied by the number of variables in the dataset

Question 23

quartiles

Answer 23

specific percentiles dividing the data into four parts

first/lower quartile corresponds to the 25th percentile (Q1)

second quartile (median) corresponds to the 50th percentile (Q2)

third (upper) quartile corresponds to the 75th percentile

fourth quartile corresponds to the maximum

Question 24

interquartile range

Answer 24

the difference between the third and first quartile

Q3 - Q1

the range for the middle 50% of the data

overcomes the sensitivity to extreme data values