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 25thpercent value while the third quartile shows the 75thpercent value.
1srquartile=$1120
3rdquartile=$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) |
(X-M) |
(X-M)(X-M) |
||||
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(1500-1604.5) |
||
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 |
  |
21021434 |
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