PSAT 10 Problem-Solving and Data Analysis. Practice it free.

Use a conversion factor with centimeters in the numerator so millimeters cancel: $80 \text{ mm} \times \dfrac{1 \text{ cm}}{10 \text{ mm}} = 8 \text{ cm}$.

$\dfrac{4}{5} = 0.8 = 80\%$.

Convert $45\%$ to a decimal and multiply: $0.45 \times 360 = 162$ chairs.

Multiply each step count by its frequency and add: $(5 \times 3) + (8 \times 2) + (11 \times 4) + (14 \times 3) + (17 \times 2) = 151$. With $14$ days, the mean is $\dfrac{151}{14} \approx 10.79$ thousand steps.

Set C has mean $10$ with values within one step of the center ($8$ through $12$), giving the smallest standard deviation, about $1.4$. Sets A, B, and D spread farther from their means.

The original mean is $\dfrac{82 + 75 + 90 + 85 + 68}{5} = 80$. The set $70\textsf{,}$ $75\textsf{,}$ $80\textsf{,}$ $85\textsf{,}$ $90$ also has mean $80$, so the means match.

In order, the original values have middle value $25$, so the median is $25$. The set $17\textsf{,}$ $23\textsf{,}$ $25\textsf{,}$ $40\textsf{,}$ $48$ also has median $25$, so the medians match.

The sample space is HH, HT, TH, TT. Exactly one head appears in $2$ of the $4$ equally likely outcomes: $\dfrac{2}{4} = \dfrac{1}{2}$.