BIOM301 Exam I - Descriptive Statistics

Define sample mean and notation.

Arithmetic average; x̄ = Σx/n.

Define sample median.

Middle ordered value; average of two middles if n is even.

Define sample mode.

Most frequent value(s); can be multimodal or none.

When do mean=median=mode?

For unimodal, perfectly symmetric distributions.

Effect of skew on mean vs median.

Mean pulled toward tail; median more robust.

Define range.

Max − Min (add a decimal place when computed).

Define sample variance (s^2).

Average squared deviation from the mean: s^2=Σ(x−x̄)^2/(n−1) for sample.

Define sample standard deviation (s).

Square root of sample variance; typical average deviation in same units as data.

Why is s usually reported rather than s^2?

s is in original units; s^2 is in squared units.

Boxplot: what five numbers?

Min, Q1, Median, Q3, Max (often show outliers).

What is a percentile?

Value below which a given percent of observations fall.

Interpretation: 's large, x̄ same'.

Greater dispersion/spread while center unchanged.

Reporting center when outliers suspected.

Use median instead of mean.

Add one extra decimal place rule.

Carry one more decimal in calculated statistics than measurement precision.