Question

or an uw we process of calculatul UE ICIUt us. 1. The homicide rates (number of assault deaths per 100,000 persons) from 6 developed nations are as follows: 1.4 (Canada), 0.9 (Germany), 1.6 (Finland), 0.3 (Japan), 0.6 (Norway), 3.9 (USA) a) From these data, calculate the standard deviation of homicide rates. Show your work. Do not use SPSS. b) Find the median homicide rate for those six nations. Show your work. Do not use SPSS. c) Is "frequency" an appropriate descriptive statistic for homicide rates? Why or why not?

Answer 1

Part a) To calculate standard deviation, first lets assume the homicide rate to be x

Particulars	x	x-mean	(x-mean)2
Canada	1.4	- 0.05 (1.4 - 1.45)	0.0025 (-0.05 * -0.05)
Germany	0.9	- 0.55 (0.9 - 1.45)	0.3025 (-0.55 * - 0.55)
Finland	1.6	0.15 (1.6 - 1.45)	0.0225 (0.15 * 0.15)
Japan	0.3	- 1.15 (0.3 - 1.45)	1.3225 (-1.15 * -1.15)
Norway	0.6	- 0.85 (0.6 - 1.45)	0.7225 (-0.85 * -0.85)
USA	3.9	2.45 (3.9 - 1.45)	6.0025 (2.45 * 2.45)
TOTAL	8.7		8.375

Mean = Ex/n, where Ex is total of column x and n is number of observations,

= 8.7/6 = 1.45

Standard Deviation = $\sqrt$ E(x-mean)2 / n, where E(x-mean)2 is total of (x-mean)2 column and n is number of observations.

= $\sqrt{}$ 8.375/6 = 1.39 (Approx)

Part b) To calculate median, first arrange the data in ascending order (smallest to largest)

Particulars	x
Japan	0.3
Norway	0.6
Germany	0.9
Canada	1.4
Finland	1.6
USA	3.9
TOTAL	8.7

Now, median in case of even number of observation is Average (mean) of the two middle most numbers in the data i.e. = 1.15

0.9 +1.4

Part c - Frequency refers to the number of times an observation occurs in a data set. In case of homicide rates, the data is interpreted as No of deaths per 100,000 i.e. No of times an event has been repeated in a population of 100,000. Such interpretation is nothing but frequency of homicide rates per 100,000. Therefore, frequence is an appropriate descriptive stastic for homicide rates.

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