Question 471·Hard·Math

The mean is the total divided by the number of readings. Every original temperature is at least $18\,^{\circ}\text{C}$, so $0\,^{\circ}\text{C}$ is below the original mean. Adding a value below the mean lowers it, so the new mean is less than the original mean.

Each frequency counts how many days had that temperature. Type $4+5+6+9$ for the rows from $18\,^{\circ}\text{C}$ through $21\,^{\circ}\text{C}$. Desmos shows $24$, so the first $24$ positions in the original ordered data are below $22\,^{\circ}\text{C}$.

The table has ten readings of $22\,^{\circ}\text{C}$. They follow the first $24$ readings, so original positions $25$ and $26$ both hold $22\,^{\circ}\text{C}$.

The median is the middle reading in order. Of $51$ readings, the 26th has $25$ readings on either side. Position $26$ holds $22\,^{\circ}\text{C}$, so that's the original median.

The new $0\,^{\circ}\text{C}$ goes before every original reading. It shifts each original reading forward one position, so original positions $25$ and $26$ become new positions $26$ and $27$. Both still hold $22\,^{\circ}\text{C}$.

With $52$ readings, the median is the average of positions $26$ and $27$. Both are $22\,^{\circ}\text{C}$, so the median stays the same. The new data set has a lower mean and an equal median. Choice D.