Question

What percentage of the general U.S. population have bachelor's degrees? The Statistical Abstract of the United States, 120th Edition, gives the percentage of bachelor's degrees by state. For convenience, the data are sorted in increasing order. 17 18 18 18 19 20 20 20 21 21 21 21 22 22 22 22 22 22 23 23 24 24 24 24 24 24 24 24 25 26 26 26 26 26 26 27 27 27 27 27 28 28 29 31 31 32 32 34 35 38
(a) Select the box-and-whisker plot.
(b) Find the interquartile range.
IQR =
(c) Illinois has a bachelor's degree percentage rate of about 26%. Into what quarter does this rate fall?

below Q1between Q1 and the median between the median and Q3above Q3

Answer 1

Answer:

a) Figure attached

b) $Q_1 = \frac{22+22}{2}= 22$

$Q_3 = \frac{27+27}{2}= 27$

$IQR = Q_3 -Q_1= 27-22 =5$

c) between the median and Q3

Step-by-step explanation:

For this case we have the following data:

17 18 18 18 19 20 20 20 21 21 21 21 22 22 22 22 22 22 23 23 24 24 24 24 24 24 24 24 25 26 26 26 26 26 26 27 27 27 27 27 28 28 29 31 31 32 32 34 35 38

Part a

We can construct the boxplot with the following R code:

> x<-c(17, 18, 18, 18, 19, 20, 20, 20, 21 ,21, 21, 21, 22, 22, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 24, 24, 24, 24, 25, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 28, 28, 29, 31, 31, 32, 32, 34, 35, 38)

> boxplot(x,main="Boxplot of data")

> summary(x)

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

 17.00   22.00   24.00   24.76   27.00   38.00

The results are on the figure attached.

The mean >Median so then we can conclude that the distribution is slightly skewed to the right.

Part b

For this case since we have 50 data values in order to find the the Q1 we use the following values 17, 18, 18, 18, 19, 20, 20, 20, 21 ,21, 21, 21, 22, 22, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 24, 24

And the Q1 would be the average between position 13 and 14 and we got:

$Q_1 = \frac{22+22}{2}= 22$

For the Q3 we need to use the following data values: 24, 24, 24, 24, 25, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 28, 28, 29, 31, 31, 32, 32, 34, 35, 38

And the Q3 would be the average between position 13 and 14 and we got:

$Q_3 = \frac{27+27}{2}= 27$

So then $IQR = Q_3 -Q_1= 27-22 =5$

Part c

For this case we have a value of 26 and if we see this value is between the meadian and Q3 since the median = 24 and Q3 = 27

between the median and Q3