Question

The average wind speeds for one year at 44 climatic data centers around the United States are as follows:
9.0, 6.9, 9.1, 9.2, 10.2, 12.5, 12.0, 11.2, 12.9, 10.3, 10.6, 10.9, 8.7, 10.3, 10.6, 10.9, 8.7, 10.3, 11.0, 7.7, 11.4, 7.9, 9.6, 8.0, 10.7, 9.3, 7.9, 6.2, 8.3, 8.9, 9.3, 11.6, 10.6, 9.0, 8.2, 9.4, 10.6, 9.5, 6.3, 9.1, 7.9, 9.7, 8.8, 6.9, 8.7, 9.0, 8.9, 9.3

a) Make a stem plot of the average wind speeds data. The frequency in the stem for 9 to 9.9 is?

b) The first quartile for the wind speed data set is?

Answer 1

The stem and leaf diagram is shown below

There are a total of 48 data

Question a:
The frequency in the stem for 9 to 9.9 is 13 data

Question b:
The location of the first quartile is given by $\frac{n+1}{4}$, where 'n' is the number of data

We have n = 48

Location of the first quartile is at $\frac{48+1}{4}= \frac{49}{4}= 12.25$ rounded down to 12

The value of the lower quartile is on the $12^{th}$ on the diagram which is 8.7