Question

Use the data for two Sydney suburbs to answer questions 1-5:            

1     Using Excel or other appropriate software, produce two separate histograms for the median rental prices of the two selected suburbs, respectively.    

       Use an appropriate number of bins for your histogram and remember to label the axes. Describe and compare the two histograms, including the central location, dispersion and skewness. [1 mark]     

            

2     Compute the sample means and sample standard deviations of the median rental prices of the two selected suburbs, respectively. No need to show computational steps. [1 mark]   

Artarmon	Chatswood
570	730
660	680
660	920
595	1100
500	880
610	840
600	750
600	540
600	490
590	630
690	600
625	600
610	1200
600	900
595	800
550	730
680	700
500	675
580	660
650	580
530	820
550	700
490	680
665	610
680	1200
580	900
680	880
670	870
585	850
660	800
500	800
595	790
490	780
530	780
565	750
570	750
580	750
595	720
600	720
600	700
610	680
625	660
660	650
680	650
690	650
580	610
585	600
650	595
665	580
590	580

Answer 1

The histogram for the median rental prices of the Artarmon suburb is:

The histogram for the median rental prices of the Chatswood suburb is:

The descriptive statistics for the Artarmon suburb is:

	Artarmon
count	50
mean	602.30
sample standard deviation	55.37
sample variance	3,065.52
minimum	490
maximum	690
range	200
skewness	-0.28
kurtosis	-0.51
coefficient of variation (CV)	9.19%
1st quartile	580.00
median	600.00
3rd quartile	657.50
interquartile range	77.50
mode	600.00

The descriptive statistics for the Chatswood suburb is:

	Chatswood
count	50
mean	742.20
sample standard deviation	149.87
sample variance	22,461.39
minimum	490
maximum	1200
range	710
skewness	1.28
kurtosis	2.22
coefficient of variation (CV)	20.19%
1st quartile	650.00
median	720.00
3rd quartile	800.00
interquartile range	150.00
mode	750.00

The central location for the Artarmon suburb is 602.30, the dispersion is 200 and the skewness is -0.28.

The central location for the Chatswood suburb is 742.20, the dispersion is 710 and the skewness is 1.28.

Therefore, we can conclude that the central location is greater for the Chatswood suburb. The dispersion is greater for the Chatswood suburb. The skewness is also greater for the Chatswood suburb.

The sample means for the Artarmon suburb is 602.30 and the sample standard deviation is 55.37.

The sample means for the Chatswood suburb is 742.20 and the sample standard deviation is 149.87.