Measures of Dispersion
Measuresof Dispersion
Whereasmean, mode, and median are measures of central tendency, there arealso measures of dispersion or spread in statistics, referred to asvariability of scatter. Measures of dispersion include standarddeviation, variance, interquartile range, and range. They measure thedegree to which a statistical data is either squeezed together orscattered. The most commonly used are range, interquartile range,variance, and standard deviation.
Rangeshows the difference between the highest and the lowest figure orentry. The lowest in this case is $32 while the highest is $2409.Therefore, the range is $2377.
Standarddeviation is calculated by first calculating the variance, which isobtained by
Where,X is the mean, M is the data, while n is the population
Populationmean equals total divide by the population size, which comes to: $(89992/60) = $1499.86
ThusApproximately $1500
Scomes to $ 592
Coefficientof skewness is obtained by,
WhereMd is median and S is standard deviation
=0.52956
Thefirst quartile shows the 25^{th}percent value while the third quartile shows the 75^{th}percent value.
1srquartile=$1120
3^{rd}quartile=$1913
Interpretationsand Conclusion
Thestandard deviation of $ 592 in the bank balances here shows that thevalues are values in the population are $592 close or far from thepopulation mean. In this case, they are not so concentrated aroundthe mean or average. The big margin in the standard deviation of bankbalances could be informed by outlies, i.e. figures that are tooextreme like $32 and $2409
Thedistribution is negatively skewed or skewed to the left. Thus thedistribution is in such a way that those balances that fall below themean are more than those that fall above the mean
Appendix 

Standard deviation 

Value (X) 
(XM) 
(XM)(XM) 

32 
1157 
1338649 

137 
920 
846400 

167 
752 
565504 

343 
610 
372100 

580 
494 
244036 
Mean 
1499.866667 

634 
456 
207936 

740 
282 
79524 

748 
180 
32400 

765 
26 
676 

789 
6 
36 

890 
1 
1 

1006 
93 
8649 

1044 
208 
43264 

1053 
284 
80656 

First quartile 
1120 
386 
148996 
Variance 
350357.23 

1125 
413 
170569 
Standard deviation 
591.909 

1169 
375 
140625 
Approximately 
592 

1218 
162 
26244 

1266 
26 
676 

1320 
116 
13456 

1326 
175 
30625 

1338 
246 
60516 

1455 
256 
65536 

1474 
385 
148225 
Median 
1604.5 

1487 
458 
209764 

1494 
489 
239121 

1501 
495 
245025 

1526 
576 
331776 

1554 
625 
390625 
Skewsness 
3(15001604.5) 

Second quartile 
1593 
656 
430336 
592 

1616 
704 
495616 

1622 
875 
765625 

1645 
909 
826281 

1675 
1468 
2155024 

1708 
1363 
1857769 

1735 
760 
577600 

1746 
447 
199809 

1756 
380 
144400 

1784 
174 
30276 

1790 
45 
2025 

1831 
54 
2916 

1838 
235 
55225 

1885 
290 
84100 

1886 
331 
109561 

Third quartile 
1913 
338 
114244 

1958 
644 
414736 

1989 
776 
602176 

1995 
1333 
1776889 

2051 
866 
749956 

2076 
735 
540225 

2125 
711 
505521 

2138 
331 
109561 

2144 
234 
54756 

2156 
13 
169 

2204 
122 
14884 

2215 
145 
21025 

2276 
551 
303601 

2375 
638 
407044 

2409 
715 
511225 

2557 
1057 
1117249 

89992 
  
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