Question

Below is a plot of July rainfall(in.) in Gainesville, Florida. The stem and leaf plot was made in Minitab. Find the third quartile.

Answer 1

Answer:

$Q_1= 0 , Median=Q_2= 0.0, Q_3 =0$

Step-by-step explanation:

Assuming the data in the figure attached. As we can see we have 31 values and for this case are:

0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,

0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,

0.0,0.0,0.0,0.0,0.1,0.1,0.1, 0.2,0.2,0.4,1.7

For this case we can use th following formulas in order to calculate the position for the quartiles:

$1Quartile= \frac{1}{4} (n+1) = \frac{1}{4} (31+1) = 8$

$3Quartile = \frac{3}{4} (n+1) = \frac{3}{4} (31+1) =24$

$Median= 3Quartile -1Quartile = 24-8= 16$

So then we have the positions the first quartile is on the 8th position from the data ordered, the third quartile on the 24th position and the median at the 16th position so we have:

$Q_1= 0 , Median=Q_2= 0.0, Q_3 =0$

And we can check this using the following R code:

data<c(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.1,0.1,0.1,0.2,0.2,0.4,1.7)

length(data)

[1] 31

median(data)

[1] 0

summary(data)

  Min.          1st Qu.  Median    Mean       3rd Qu.    Max.  

0.00000 0.00000 0.00000 0.09032 0.00000 1.70000

And as we can see the results are the same with the formulas.