Statistical Methods- Lectures3-4

Question 1

What are scatterplots useful for?

Answer 1

Scatterplots are useful for visualizing the relationship between two numerical variables.

Question 2

How do you describe the distribution of a quantities variable in a graph?

Answer 2

Describe the overall pattern (shape, center, spread etc.) and deviations from the pattern (e.g. Outliers)

Question 3

How do you calculate the sample mean?

Answer 3

The sample mean, denoted by x̄, can be calculated as
x̄=(x1+x2+…+xn)/n

The sample mean is a sample statistic, and serves as a point estimate if the population mean.

Question 4

What is the population mean?

Answer 4

The population mean is a population parameter computed the same way using all values in the population and is denoted by μ.

Question 5

What do histograms provide?

Answer 5

Histograms provide a view of the data density. Higher bars represent where the data is more common.

Question 6

What are commonly observed shapes of distributions?

Answer 6

Modality- Unimodal, bimodal, multimodal, uniform

Skewness- right skew(tails off to the right), left skew, symmetric

Question 7

What are outliers?

Answer 7

An outlier is an observation that lies an abnormal distance from other values in a random sample from a population.

Question 8

How do you find the sample variance?

Answer 8

The sample Variance is roughly the average squared deviation from the mean.

S^2= ∑^n i=1 (xi-x̄)^2/n-1

Question 9

Why do we use the n-1 in the calculation of variance?

Answer 9

To make the variance an unbiased estimate

Question 10

How do you find the standard deviation?

Answer 10

The standard deviation is the square root of the variance

Question 11

How can you describe the centre and spread of a distribution?

Answer 11

Spread:

• Mean
• Variance
• Standard Deviation

Centre:

• Median
• Range
• Interquartile Range

Question 12

How do you find find the interquartile range and the range of all data?

Answer 12

IQR=Q3-Q1

Range=Max value - Min Value

Question 13

What are the five number summary of the data?

Answer 13

The median, Q1, Q3, Min and Max are called the five number summary of the data

Question 14

What does the box in a box plot represent?

Answer 14

The box in a box plot represents the middle 50% of the data, and the thick line in the box is the median

Question 15

What are whiskers of a box plot?

Answer 15

Max upper whisker reach=Q3+1.5xIQR

Max lower whisker reach=Q1-1.5xIQR

A potential outlier is defined as an observation beyond the maximum reach of the whiskers

Question 16

Why is it important to look for outliers?

Answer 16

• To identify extreme skew in the distribution
• Identify data collection and entry errors
• Provide insight into interesting features of the data

Question 17

How do you describe the center and spread in skewed and symmetric distributions?

Answer 17

For skewed distributions it is often more helpful to use median and IQR to describe the center and spread meanwhile it is better to use the mean and SD for a symmetric distribution.