Question

68.45
58.58
60.36
65.48
75.43
61.26
63.39
56.98
49.77
57.02
67.40
63.42
52.29
68.20
51.48
47.93
61.21
57.31
64.42
65.56
62.91
59.82
54.99
60.30
47.28
61.52
79.46
70.35
68.77
59.70
54.20
56.38
51.07
68.89
54.39
58.37
51.49
50.61
61.42
54.31
55.41
61.75
74.12
71.57
63.71
67.07
53.85
64.22
57.44
51.29
46.46
52.39
55.47
70.41
51.77
56.36
53.36
47.32
54.81
47.93
53.80
57.54
64.97
67.87
52.25
58.29
59.82
65.60
51.67
52.50

Seventy (70) random samples of lumpy iron ore (95% particle size, 150 millimeters) were randomly sampled from a 35,000 long-ton shipload, and the percentage of iron in each sample was determined.

a. Examine descriptive statistics of the mean, median, standard deviation, first quartile, third quartile, minimum value, and maximum value. Minimally construct a boxplot, histogram and normal probability plot of the data. Comment on the shape and symmetry of the data’sdistribution

Answer 1

Following is the screen shot of excel to generate the descritpive statistics, normal probability plot and box plot:

Following is the output generated by excel:

Following is the freqeuncy distribution:

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nterpretation:

Mean is greater than median which shows the distribution is skwed to right.

Mode is 47.93. It shows that in samples 47.93% is has highest frequency.

The middle 50% data values lies between 53.47 and 64.37.

Minimum value is 46.46 and maximum value is 79.46.

The normal probability plot shows approximately a straight line so data can be assumed normally distributed.

Histogram shows that distribution is skewed to right.