Stats 1124: CH 2

• The measures of the average!
• Symbol: x(with line on top)

Median(m): the value that has the middle position when n data points are put in order

1. If graph is mound and symmetric, mean and median are the same.

2. If graph is skewed, mean moves away from the median toward the longer tail

Because it is NOT affected by an extreme observation(change).

• 1. Range
• 2. Standard Deviation

Range(R) = MAX - MIN , it gives us the spread of the entire data

(s): It uses all the data points and describes the variation around the mean.

It is a concept not a calculation!

Idea: The number of observations that are free to vary after the sample mean has been calculated

(Q3 - Q1): It gives us the spread of the middle 50% of the data

(Q1 - 1.5 x IQR) and (Q3 + 1.5 x IQR)

Any values that fall outside this range (Q1 - 1.5 x IQR) and (Q3 + 1.5 x IQR)

They are best used by a side-by-side comparison

Bceause too many points(50) or too little (2) will cause the shape to look unappealing.

• 50 points = not summarized enough
• 2 points = too summarized

• 1. large dataset
• 2. left inclusion
• 3. no overlap

• 1. Centre:(Midpoint)
• 2. Spread:(Range)
• 3. Outlier: (unusual points)
• 4. Shape:( Symmetrical, skewed right and left)

Mean can be increased by adding more data points and decreased by removing datapoints

• Check if it affects the outliers.
• Mean is sensitive to the influence of extreme observations(Changes a lot when something is added or deleted), therefore, NOT RESISTANT.

If something is resistant to something then it DOESN'T change a lot, if it is NOT resistant to something then it CHANGES easily.

Range is NOT a resistant outlier.

Median IS resistant