Each repeated data value counts separately in a mean or median

An extreme value pulls the mean more than the median

For $[4,4,7,9,16]$, the mean is $8$ and the median is $7$. The repeated $4$ represents two observations and must appear twice. The large value $16$ pulls the mean upward more than it affects the median.

Type mean or median and put the list inside parentheses. Desmos displays the function name and evaluates the list. Read which statistic the problem requests before copying a result.

$\displaystyle \operatorname{mean}\left(\left[4,4,7,9,16\right]\right)$

Total divided by the number of observations: 8.

$\displaystyle \operatorname{median}\left(\left[4,4,7,9,16\right]\right)$

Middle value in sorted order: 7.

$\displaystyle \operatorname{stdevp}\left(\left[4,4,7,9,16\right]\right)$

Population standard deviation, a measure of spread.

A frequency is a count, not another measurement

Suppose the values $2,5,9$ have frequencies $3,2,1$. The data set is $[2,2,2,5,5,9]$, so its mean is $(2\cdot3+5\cdot2+9\cdot1)/6=25/6$. Taking the mean of only $2,5,9$ would discard the frequencies.

In official SAT Desmos, lists and totals can calculate weighted sums. For a small frequency table, expanding the repeated values is often easier to check. For grouped intervals, a midpoint-based mean is an estimate unless the actual observations are known.

Adding a constant shifts the center; multiplying scales both center and spread

Adding $5$ to every value adds $5$ to both mean and median, while the standard deviation stays the same. Multiplying every value by $3$ multiplies center and standard deviation by $3$.

Use stdevp for population standard deviation and stdev for sample standard deviation when that distinction is specified. Many SAT spread questions need a comparison rather than a numerical calculation. A wider spread around the center means a larger standard deviation.

A regression shows association, not cause and effect

A regression can describe association but cannot establish cause and effect. Random sampling supports generalizing to a population; random assignment supports a causal comparison in an experiment.

For probability, identify the appropriate total before dividing. A conditional probability uses the total within the stated group, which may differ from the whole table's total.

Keep practicing the connected skills