Question

2. Comparing smaller data sets using box plots Two data sets describing the fraction of protein recovered from thirteen test samples by each of two different methods are given in the table below Method1 Method 2 0.32 0.35 0.37 0.39 042 0.47 0.51 0.58 0.60 0.62 0.65 0.68 0.75 0.25 0.40 0.48 0.55 0.56 0.58 0.60 0.65 0.70 0.76 0.80 0.91 0.99 (a) Construct boxplots of the two sets of data. Compare the whisker lengths in the box plots of the two cases in either direction and the data ranges in the two cases. Are there any outliers in either case? (b) Compare the medians, means, standard deviations and SDOM (std. deviation of the mean) or SE Mean as well as the interquartile range (IQR) for the two sets of data. Which of these statistical parameters does not appear on the boxplot? Does the difference between median and mean for each case confirm your conclusions of part (a) regarding the symmetry or skewedness of the two cases? Be specific here Note: Don't just take freestyle MINITAB output; present your results with the correct number of decimal places

Answer 1

Answer:

a).

whisker length of Method2 is longer in both directions compared to Method 1. There is no outliers for both data set. Range of Method2 is longer compared to Method 1.

b).

MINITAB output

Descriptive Statistics: Method 1, Method 2

Statistics

Variable	N	Mean	SE Mean	StDev	Minimum	Q1	Median	Q3	Maximum	Range
Method 1	13	0.5162	0.0389	0.1403	0.3200	0.3800	0.5100	0.6350	0.7500	0.4300
Method 2	13	0.6331	0.0562	0.2028	0.2500	0.5150	0.6000	0.7800	0.9900	0.7400

Variable	IQR
Method 1	0.2550
Method 2	0.2650

Result with 2 decimals.

Descriptive Statistics: Method 1, Method 2
Statistics
Variable	N	Mean	SE Mean	StDev	Minimum	Q1	Median	Q3	Maximum	Range
Method 1	13	0.52	0.04	0.14	0.32	0.38	0.51	0.64	0.75	0.43
Method 2	13	0.63	0.06	0.20	0.25	0.52	0.60	0.78	0.99	0.74
Variable	IQR
Method 1	0.26
Method 2	0.27

Mean, standard deviation and SE of mean does not appear on the boxplot.

For method 1, mean is > median, data is positively skewed.

For method 2, mean is > median, data is positively skewed.