Section 2 (Pgs 20-25)

Question 1

What are the 3 most common measures of central tendency?

Answer 1

Mean
Median
Mode

Question 2

Most common measures of spread or variability? (4)

Answer 2

Standard deviation
Variance
Range
Semi-interquartile range

Question 3

Symbol for mean of population?

Answer 3

µ (mu)

Question 4

Symbol for standard deviation of population?

Answer 4

σ (sigma)

Question 5

Symbol for mean of a sample?

Answer 5

x̅ (ex bar)

Question 6

Symbol for standard deviation of a sample?

Answer 6

s

Question 7

What is the mean?

Answer 7

The sum of data values divided by the number of data values

Question 8

How do you calculate the mean from a frequency table?

Answer 8

Sum of frequencies multiplied by the midpoint of the group divided by total number of observations

Question 9

How would you describe the sample mean as an estimator of the population mean?
Why?

Answer 9

Unbiased estimator

The mean of all possible sample means than can be selected from a population is equal to the population mean

Question 10

Why is the mean an efficient summary statistic?

Answer 10

It uses all the data

Question 11

What is a negative point about using the mean?

Answer 11

It is sensitive to extreme values so would not be used to summarise data with extreme values

Question 12

What is the median?

Answer 12

The middle value when the data is ranked in numerical order

Question 13

If the mean and median are the same, what does this say about the data?

Answer 13

The distribution is symmetrical and there are no extreme values

Question 14

When is the median more appropriate to use than the mean as a measure of central tendency?

Answer 14

When there are extreme values

Question 15

Is the median affected by extreme values?

Answer 15

No

Question 16

What is the mode?

Answer 16

The most frequently occurring value in a data set

Question 17

What is the mode useful for?

Answer 17

It is the only measure of centre for qualitative data

Question 18

Is the mode sensitive to extreme values?

Answer 18

No, however it is wasteful of the data as it only uses one observation

Question 19

When is the mean used?

Answer 19

As the measure of centre for quantitative data, unless the distribution of the data is skewed

Question 20

When is the median used?

Answer 20

As the measure of centre for qualitative data when the distribution of the data is skewed/ there are extreme values

Question 21

When is the mode used?

Answer 21

As the measure of the centre for qualitative data

Question 22

What does the variance and standard deviation measure?

Answer 22

The spread of the data above the mean

Question 23

How is the standard deviation related to the variance?

Answer 23

It is the square root of the variance

Question 24

What is the variance?

Answer 24

The average of the squared deviations for the mean

Question 25

How do you calculate the variance from a frequency table?

Answer 25

Sum of frequencies multiplied by midpoint - mean squared, divided by n -> same as variance equation with f before bracket

Question 26

How would you describe the use of sample variance to estimate the population value?

Answer 26

Biased

Average of all sample variances is not equal to the population value

Question 27

What does the population variance equal, in terms of the sample variance?

Answer 27

Sample variance X n/ n-1

Question 28

How can the variance equation be changed to ensure that the sample variance provides an unbiased estimate of the population value?

Answer 28

n-1 is used as the denominator

Question 29

How does the standard deviation relate to the spread of data?

Answer 29

The larger the standard deviation, the wider the spread of the data

Question 30

If the standard deviation = 1, how many standard deviations would you expect 95% of the data to lie within?

Answer 30

2

Question 31

What would a standard deviation of 0 mean?

Answer 31

There is no variation in the data -> all data is the same

Question 32

What is the range a measure of?

Answer 32

The extremes (not the variability) -> not used very often as a measure of spread

Question 33

What is the inter-quartile range?

Answer 33

The difference between the first and third quartiles

Question 34

Is the inter-quartile range affected by extreme values?

Answer 34

No (it only includes the middle 50% of observations)

Question 35

What is the most commonly used measure of spread of data about the mean for continuous data and most discrete observations?

Answer 35

Standard deviation

Question 36

What is used preferentially to the standard deviation when there are outlying observations?

Answer 36

Inter-quartile range

Question 37

What is the word used to describe data that is not symmetrical?

Answer 37

Skewed

Question 38

What is it called when most values lie towards the bottom of the range and there is a tail to the right?

Answer 38

Positively skewed

Question 39

What is it called when most values lie towards the top fo the range and there is a tail to the left?

Answer 39

Negatively skewed

Question 40

Are positively or negatively skewed data more common?

Answer 40

Positively - negatively skewed data is rare

Question 41

What does the coefficient of skewness do?

Answer 41

Indicates if the data is symmetrical or positively or negatively skewed

Question 42

What does the coefficient of skewness equal if the data is symmetrical?

Answer 42

0

Question 43

What does a coefficient of skewness greater than 0 indicate?

Answer 43

Positive skewness

Question 44

What does a coefficient of skewness less than 0 indicate?

Answer 44

Negative skewness

Question 45

What is kurtosis?

Answer 45

A measure of the peakedness of a distribution

Question 46

What does a value of 0 for the kurtosis indicate?

Answer 46

A shape close to the normal distribution

Question 47

What does a positive value for the kurtosis indicate?

Answer 47

A relatively peaked distribution