Question

In an attempt to measure the effects of acid rain, researchers measured the pH (7 is neutral and values below 7 are acidic) of water collected from rain in Ingham County, Michigan.

5.47 5.37 5.38 4.63 5.37 3.74 3.71 4.96 4.64 5.11

5.65 5.39 4.16 5.62 4.57 4.64 5.48 4.57 4.57 4.51

4.86 4.56 4.61 4.32 3.98 5.70 4.15 3.98 5.65 3.10

5.04 4.62 4.51 4.34 4.16 4.64 5.12 3.71 4.64 5.59

(a)

Find the sample mean and sample standard deviation of these measurements.

  

(b)

Find the quartiles and median of the data.

(c)

Draw a box plot for the data.

(d)

Should any points be considered potential outliers, if there is any outliers, calculate their values?

Answer 1

We use Minitab to solve this question-

Welcome to Minitab, press F1 for help.

MTB > Describe 'Measurements';
SUBC>   Mean;
SUBC>   StDeviation;
SUBC>   QOne;
SUBC>   Median;
SUBC>   QThree;
SUBC>   GBoxplot.

Descriptive Statistics: Measurements

Variable       Mean StDev     Q1 Median     Q3
Measurements 4.720 0.637 4.325   4.635 5.370

Boxplot of Measurements

________________________________________________________________________________________________________________________

a) Sample Mean = 4.720, Sample standard deviation = 0.637
b) First quartile(Q1) = 4.325
   Second quartile(Q2) = Median = 4.635
   Third quartile(Q3) = 5.370
d)
Inter quartile range (IQR) = Q3 - Q1 = 5.370 - 4.325 = 1.045
Q1 - 1.5 * IQR = 2.76
Q3 + 1.5 * IQR = 6.94
Any value less than the 2.76 and more than the 6.94 is considerd as a outlier.
From given sample we observe that there is no any sample which is less than the 2.76 and more than the 6.94 therefore their is no any outlier.

c)