HSS.ID.A.2 math practice. Learn by doing.

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 $77$, so the median is $77$. The set $70\textsf{,}$ $73\textsf{,}$ $77\textsf{,}$ $91\textsf{,}$ $97$ also has median $77$, so the medians match.

Set C includes the outlier $10$ while the other values cluster near $24$, so values are far from the mean $22$. Its standard deviation is about $6.3$, greater than the evenly spaced sets A, B, and D.

Six days with a mean of $23$ laps total $6 \times 23 = 138$. Since $20 + 24 + 18 + 22 + 26 = 110$, $x = 138 - 110 = 28$.

Mean $= \dfrac{4 + 7 + 10}{3} = \dfrac{21}{3} = 7$.

The original mean is $\dfrac{18 + 22 + 30 + 20 + 35}{5} = 25$. The set $15\textsf{,}$ $20\textsf{,}$ $25\textsf{,}$ $30\textsf{,}$ $35$ also has mean $25$, 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.

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.