Question

Exercise 1. [10 points) Descriptive Statistics A team of researcher has collected a sample of water from a river and wants to represent the levels of lead pollution, in parts per liter. Two histograms are produced: 5 3 Count 1 20 40 60 80 100 Lead parts/liter 0.025 0.020 0.015 Frequency 0.010 0.005 0.000 20 40 60 80 100 Lead parts/liter

a) Which of the two graphs presented above is constructed according to the principle of areas being proportional to frequencies? Do they visually convey the same information? Comment on what you may find misleading

b) Use the appropriate graph to compute the sample median with the information you have. Is the quantity you computed necessarily equal to the median in the raw data?

Answer 1

a) Which of the two graphs presented above is constructed according to the principle of areas being proportional to frequencies? Do they visually convey the same information? Comment on what you may find misleading

The graph a) is constructed as per the the proportional frequencies, since the sum of all frequencies in the second graph don't add up to 1.

They don't convey the same meaning by visual inspection. For instance, the frequencies in the 50-80 interval is 3 each but the height of the bars in the second graph doesn't correspond to this frequency when comparing the frequency of 30-40 class.

b). The total frequency is 30(by adding all the heights). Therefore the median is and this roughly falls in the class 50-60. Therefore the median class is 50-60.The frequencies just above this is 13.

*N = 15 2

Therefor the median is =50+

10 50+ (15-13) = 50 +6.67 = 56.67 3

The median =56.67.

This median so calculated will rarely be the same as that of the raw data since, it is derived from a frequency distribution.

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The frequency distribution is just given for information>

LL	UL	Frequency	Cumulative frequency
10	20	1	1
20	30	4	5
30	40	3	8
40	50	5	13
50	60	3	16
60	70	3	19
70	80	3	22
80	90	4	26
90	100	4	30
	Total	30