3.4.171 quartiles

An article by a researcher reported on a​ long-term study of the effects of hurricanes on tropical streams in forests. The study shows that one particular hurricane had a significant impact on stream water chemistry. The following table shows a sample of 10 ammonia fluxes in the first year after the hurricane. Data are in kilograms per hectare per year. Complete parts​ (a) through​ (e) below.
Recommanded find quatiles mannually in Excel since there is inconsistent approach in R
  • even number of data set - type 5
  • odd number of data set - type 1

First, we need to import the data from Excel. (For simplicity, this imports mannual by hand, we can get the same result by importing dataset from Excel)

x <- c(88, 171, 64, 159, 89, 84, 180, 126, 123, 91)
x
##  [1]  88 171  64 159  89  84 180 126 123  91

(a). Obtain and interpret the quartiles

Since we have even number of

summary(x, quantile.type=5)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    64.0    88.0   107.0   117.5   159.0   180.0
quantile(x, type=5)
##   0%  25%  50%  75% 100% 
##   64   88  107  159  180
part A

(b).Determine and interpret the interquartile range​ (IQR). We use the formula $IQR = Q_3-Q_1 $

159-88
## [1] 71

(c). Find and interpret the​ five-number summary.

We can see the summary from part (a)

To interpret five-number summary, we plot boxplot of data

boxplot(quantile(x, type=5))
(d). Identify potential​ outliers, if any. Choose the correct answer below​ and, if​ necessary, fill in the answer box to complete your choice
  • Lower limit = \(Q_1 - 1.5.IQR\)
  • Upper limit = \(Q_3 + 1.5.IQR\)
    Lower limit
88 - 1.5 * 71
## [1] -18.5

Upper limit

159 + 1.5 * 71
## [1] 265.5

Sort our data

sort(x)
##  [1]  64  84  88  89  91 123 126 159 171 180

Hope that helps!