2012 2 exerc Desvio Padrao Moda e Mediana Solucao

2012_2 ex 1

4
4
6
6

6
7
7
8

8
8
9
10

11
12
12
13

mínimo = máximo = n= Amp = máx - mín =
K = raiz(n) = 4,4721 = h = Amp/(k - 1) = 3,6667 =
Limite Inferior = mínimo - h/2 =

13
13
14
15

Elemento Central =
Li da classe Med = fantac = fmed =
Md = 6 + (20/2- 5).4
7

10,5
2
6
6
5
10
7
14
= 8,8571 total

----|
----|
----|
----|

xm =
Cl Modal =
Li Cl Mo = d1 = d2 =

Mo = 10 +

0 .4=
0+6

7
10
0
6
10,00

2

6,0
10,0
14,0
18,0

Freq
Abs
5
7
7
1
20

Média =

s = 12,1599
2
s = 12,7999

Freq
Acum
5
12
19
20
----

pontos = 4

4
15
20
11,00
4
4,0
2,0

Q3 = 12,25

xi

xi . fi

xi - xm

(xi - xm )

2

(xi - xm )2.fi

4
8
12
16
----

20
56
84
16
176

-4,8
-0,8
3,2
7,2
----

23,0400
0,6400
10,2400
51,8400
----

115,2000
4,4800
71,6800
51,8400
243,2000

(3.n/4)+1/2 = 15,500

176,00 = 8,8
20

Q3 = 10 + s = 3,4871 s = 3,5777

(3.20/4 - 12).4
7

= 11,7143

2012_2 ex 2

100
104
116
120

130
134
138
140

140
146
150
150

150
170
176
176

180
184
186
188

mínimo = máximo = n= Amp = máx - mín =
K = raiz(n) = 4,4721 = h = Amp/(k - 1) = 29,3333 =
Limite Inferior = mínimo - h/2 =

Elemento Central =
Li da classe Med = fantac = fmed =
Md = 143,5 + (20/2- 9).29
5

10,5
143,5
9
5
= 149,3

85,5
114,5
143,5
172,5
total

----|
----|
----|
----|

xm =
Cl Modal =
Li Cl Mo = d1 = d2 =

Mo = 114,5 +

5
5+2

7
114,5
5
2
. 29 = 135,2143

2

114,5
143,5
172,5
201,5

Freq
Abs
2
7
5
6
20

Média =

s = 830,4887
2
s = 874,1957

Freq
Acum
2
9
14
20
----

100
188
20
88,00
4
29,0
85,5

Q3 = 176

2

xi

xi . fi

xi - xm

(xi - xm )

100
129
158
187
----

200
903
790
1122
3015

-50,75
-21,75
7,25
36,25
----

2575,5625
473,0625
52,5625
1314,0625
----

3015,00 = 150,75
20

s = 28,8182 s = 29,5668

(xi - xm )2.fi

5151,1250
3311,4375
262,8125
7884,3750
16609,7500

(3.n/4)+1/2 = 15,500

Q3 = 172,5 +

(3.20/4 - 14).29
6

= 178,3

2012_2 ex 3

1
4
5
7

2
4
5
8

2
4
6
8

2
4
6
9

mínimo = máximo = n= Amp = máx - mín =
K = raiz(n) = 4,4721 = h = Amp/(k - 1) = 2,6667 =
Limite Inferior = mínimo - h/2 =

3
5
7
9