Data analysis practice

Averages and range

• Mean = sum of values ÷ number of values
• Median: the middle value after sorting (the mean of the two middle values if the count is even)
• Mode: the most frequent value
• Range = maximum − minimum

For $4, 7, 7, 8, 9, 10$: median $7.5$, mode $7$, range $6$.

Frequency tables

A frequency table groups data into classes. The middle of a class is its midpoint. The mean from a table is the sum of (midpoint × frequency) divided by the total frequency; the mode is the midpoint of the most frequent class.

Relative frequency

Relative frequency = class frequency ÷ total. The cumulative relative frequency adds up the classes from the first one.

After many trials, the relative frequency estimates the probability: if a thumbtack lands point up $210$ times in $500$ tosses, expect about $0.42 \times 2000 = 840$ in $2000$ tosses.