Stats Chapter 2 Lecture 3

average of the two middle values

for the median, if number is even and there is not one middle number, then take the ______

median

the middle value of a set of numbers

mean

the average of a set of numbers

ȳ

the sample mean symbol is _____

Σyᵢ / n (sum of all values​ divided by number of values)

ȳ = ______

balance point

The mean is the ______ of the distribution

is

is not

Mean → ______ sensitive to outliers

Median → ______ sensitive to outliers

median

the _______ is usually better for skewed data

symmetric

left-skewed

right-skewed

Mean ≈ Median

Mean < Median

Mean > Median

high, right/up

low, left/down

Right-skewed: The long tail has ______ values → pulls the mean to the _______

Left-skewed: The long tail has ______ values → pulls the mean to the _______

mean

median

Symmetric data → use the ______

Skewed data → use the _______

sample mean

population mean

ȳ (y-bar) = _______

μ (mu) = ________

• median (Q2)

• below, Q1

• above, Q3

• minimum

• maximum

how to find the 5-number summary:

• Find the ______

• Look at the values ______ the median → find their median → ______

• Look at the values ______ the median → find their median → ______

• The smallest value = _______

• The largest value = ________

Maximum − Minimum

for 5-number summary, range = _______

Q3 − Q1

for 5-number summary, IQR = ______

min, Q1, median, Q3, max

5-number summary order:

entire

middle 50%

Range = ______ spread
IQR = ______ spread

Fence Method

use the ______ to identifying outliers objectively

Q3+1.5(IQR)

Q1−1.5(IQR)

Upper fence formula: ______

Lower fence formula: ______

above

below

Any value ______ the upper fence → outlier

Any value ______ the lower fence → outlier

symmetric

right-skewed

left-skewed

Median centered in box, whiskers similar length then roughly _______
Median closer to Q1, long right whisker then ______
Median closer to Q3, long left whisker then _______

Q1 to Q3, median (Q2), whiskers, outliers

for constructing a boxplot, draw a box from ______ (spans the middle 50% of the data), then draw a line inside the box at the ______, then draw the ______ extending to the most extreme non-outlier values, last plot any ______ separately

standard boxplot

whiskers from Q1 to min and Q3 to max

Modified boxplot (preferred)

Whiskers extend to the most extreme non-outlier values and Outliers plotted individually as dots or asterisks

median

middle of ordered data; robust to outliers; use for skewed distributions

mean

sum of data/n; sensitive to outliers; use for symmetric distributions

Min, Q1, Median, Q3, Max - four equal quarters

5-number summary (short)

Q3 − Q1: spread of the middle 50%

IQR = ______

fence method

outliers lie beyond Q3+1.5(IQR) or below Q1−1.5(IQR)

boxplot

visual of the 5-number summary; modified version shows outliers explicitly