Question

Practice problems 2 – Central Tendency

1. Here is a random sample of seven rents ($) from the data collected. (In case you are wondering, I used a computer to generate random samples).

$0.00 $600.00 $650.00 $650.00 $1000.00 $570.00 $0.00

1. a) Calculate the average rent of this random sample.

2. b) What is the median of this random sample?

2. What are the mean, median, and mode of the following distributions? Which measure of central tendency best reflects each distribution and why?

   1. a) 1, 1, 1, 100, 100, 100

   2. b) 2, 3, 4, 6, 100

   3. c) 1, 1, 1, 1, 1, 1, 5, 5, 6, 8, 9

3. You are told that a sample of 17 cans of tuna is taken to test if too much tuna (more weight) occurs too often. The personnel tells you that although they do not know much about the stated study, they do know the distribution of weight of tuna per can is highly skewed. If asked for a measure of central tendency, which one would you give preference to? Why?

4. A company that created a new website, hired an analyst to increase the number of unique visitors to the website coming from internet search queries. Let’s say the number of clicks related to the website where an average of 4 per day BEFORE the analyst was hired and AFTER the analyst makes some changes the average clicks per day where 8. Would you say there is a worthwhile difference? Explain

5. Let’s say you work for a government agency that has sample median income of Mayaguez residents for every year from 1920 to 2011 with the exception of the year 1980. A supervisor suggests taking the data of all those years and then taking the median as the median income of 1980. What do you think of this recommendation?

Answer 1

1)

a) average =( $0.00+ $600.00 +$650.00+ $650.00+ $1000.00+ $570.00+ $0.00)/7 = $495.714

b) median is the 4th observation when the sample is arranged in the ascending order, which is $600

2)

a)

mean = 50.5

median = 50.5 (average of 3rd and 4th observations)

mode = 1 and 100 (bimodal)

for this sample mode has all data set so it is preferable.

b)

mean = 23

median = 4

mode is ill defined

median is preferable since it free from extreme value 100

c)

mean = 3.545

median =1

mode = 1

mean is preferable since both median and mode don't represent the last six data points

3)

median, since middle part of data represents more better than other two measures of central tendency in skewed distribution

4)

yes, the average increased.. it implying that the change brought by analyst is effective..

5)

This suggestion is good if 1980 is a normal period. If 1980 has some disaster or any other abnormality then we cannot prefer that.

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