Find Mean, median, standard deviation,maximum and minimum. Number of divorces in February of 1996 per state....

Find Mean, median, standard deviation,maximum and minimum. Number of divorces in February of 1996 per state. 548,315,239,214,821,0,1290,1823,2654,3852,0,2678,4220,1573,1056,957,2076,164,218,446,1038,302,839,77,1912,528,2668,1277,3088,5003,1722,3385,1698,1143,653,0,1606,7668,360,451,263,0,887,1981,866,356,2725,1359,0,156,411,0.

Expert Solution

Solution:

x	x²
548	300304
315	99225
239	57121
214	45796
821	674041
0	0
1290	1664100
1823	3323329
2654	7043716
3852	14837904
0	0
2678	7171684
4220	17808400
1573	2474329
1056	1115136
957	915849
2076	4309776
164	26896
218	47524
446	198916
1038	1077444
302	91204
839	703921
77	5929
1912	3655744
528	278784
2668	7118224
1277	1630729
3088	9535744
5003	25030009
1722	2965284
3385	11458225
1698	2883204
1143	1306449
653	426409
0	0
1606	2579236
7668	58798224
360	129600
451	203401
263	69169
0	0
887	786769
1981	3924361
866	749956
356	126736
2725	7425625
1359	1846881
0	0
156	24336
411	168921
0	0
---	---
x=69566	x²=207114564

The sample mean is

Mean = (x / n) )
=548+315+239+214+821+0+1290+1823+2654+3852+0+2678+4220+1573+1056+957+2076+164+218+446+1038+302+839+77+1912+528+2668+1277+3088+5003+1722+3385+1698+1143+653+0+1606+7668+360+451+263+0+887+1981+866+356+2725+1359+0+156+411+0 / 52

= 69566 / 52

=1337.8077

Mean = 1337.81

Median :
Observations in the ascending order are :
0,0,0,0,0,0,77,156,164,214,218,239,263,302,315,356,360,411,446,451,528,548,653,821,839,866,887,957,1038,1056,1143,1277,1290,1359,1573,1606,1698,1722,1823,1912,1981,2076,2654,2668,2678,2725,3088,3385,3852,4220,5003,7668

Here, n=52 is even.

M=Value of(n / 2)^th observation+Value of(n / 2+1)^th observation / 2

=Value of(52 / 2)^th observation+Value of(52 / (2+1)^th observation) /2

=Value of 26^th observation+Value of 27^th observation / 2

=866+8872

=876.5

Median =876.5

The sample standard is S

S =( x² ) - (( x)² / n ) n -1

=(207114564-(69566)² 52 / 51)

=207114564-93065929.9231 /51

=114048634.0769 / 51

=2236247.727

=1495.4089

The sample standard is = 1495.41

Maximum Number = 7668

Minimum Number = 0

orchestra answered 2 years ago

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