Question

4 The data below shows the number of manufacturing plants in the UK arranged according to employment Number of Number of firms, f Cumulative frequency employees l0x 20 20(x<=50 50-x( 100 1 00<x< 200 200x 500 500x 1000 95409 15961 16688 7229 4504 2950 796 334 143871 95409 111370 128058 135287 139791 142741 143537 143871 Total a) From simply scanning the information, would you say the dataset was skewed a littlea lor? skewed to the left or skewed to the right? b) Calculate the median of the dataset. Without calculation, would you expect the mean to be above or below you answer? c) Calculate the inter-quartile range of the dataset. 5. A dataset contains the following six values 10 232 26 25 22 On the basis that this dataset is a population a Find the range b Find the population variance and standard deviation
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Answer #1

Solution5a:

range =max-min

=26-10

=16

range=16

Solution5b:

X xbar x-xbar (x-xabr)^2
10 21.167 -11.167 124.7019
23 21.167 1.833 3.359889
21 21.167 -0.167 0.027889
26 21.167 4.833 23.35789
25 21.167 3.833 14.69189
22 21.167 0.833 0.693889
total 42.13145
mean=xbar=sum of values/total obsrvations=127/6=21.167 variance=42.13145/6
variance=7.021907
standard deviation =sqrt(variance)
=sqrt(7.021907)
standard deviation'=2.64988
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