The given dot plot represents the average daily temperatures, in degrees Fahrenheit, recorded in a town during the first 15 days of September. If the dot plot is converted to a box plot, the first quartile would be drawn at
, and the third quartile would be drawn at
In order to find the first quartile and third quartile on the box plot, we need to determine the median and the interquartile range (IQR) first. We can find the median by locating the middle value in the data set, which is the dot corresponding to the 8th day. From the plot, we can see that this dot is located at 70 degrees Fahrenheit.
Next, let's find the IQR. The IQR is the range of the middle 50% of the data. In this case, the first quartile is the median of the lower half of the data set, and the third quartile is the median of the upper half.
From the plot, we can see that the 25th percentile is located at the dot corresponding to the 4th day, which is around 65 degrees Fahrenheit.
Similarly, we can see that the 75th percentile is located at the dot corresponding to the 12th day, which is around 75 degrees Fahrenheit.
Therefore, if the dot plot is converted to a box plot, the first quartile would be drawn around 65 degrees Fahrenheit, and the third quartile would be drawn around 75 degrees Fahrenheit.