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Problem Set 1

Problem # 60
Owenns Orchards sell apples in a large bag by weight. A sample of seven bag contained the following numbers of apple: 23, 19, 26, 17, 21, 24, 22.
a) Complete the mean number & Median number of apples in a bag
Sample Mean: ¯X=ΣX/n
¯X= (26+24+23+22+21+19+17)/7
¯X = 152/7
¯(X )= 22

Sample Median:
Low to high High to low
17 26
19 24
21 23
22 22 ↔ Median 22
23 21
24 19
26 17

b) Verify that ∑(X-¯X) = 0

(26-22)+(24-22)+(23-22)+(22-22)+(21-22)+(22-19)+(17-22)=

4+2+1+0-1-3-5=

= -0.2

Problem # 62
The Citizens Banking Company is studying the number of times the ATM located in a Loblaws Supermarket at the foot of Market Street is used per day. Following are the numbers of times the machine was used over each of the last 30 days.

Where:
n = 30
¯X = ?

83 64 84 76 84 54 75 59 70 61
63 80 84 73 68 52 65 90 52 77
95 36 78 61 59 84 95 47 87 60

a) Determine the mean number of time the machine was used per day:
¯X=ΣX/n
¯X = (83+64+84+76+84+54+75+59+70+61+63+80+84+73+68+52+65+90+52+77+95+36+78+61+59+84+95+47+87+60)/30
¯X = 2,116/30
¯X= 70

Problem # 68
The American Automobile Association checks the prices of gasoline before many holiday weekends. Listed below are the self-service prices for a sample of 15 retail outlets during the May 2003 Memorial Day weekend in the Detroit, Michigan area.
1.44 1.42 1.35 1.39 1.49 1.49 1.41 1.46
1.41 1.49 1.45 1.48 1.39 1.46 1.44
Where:
N = 15
μ = ?
a) What is the Arithmetic Mean selling price?
μ= ΣX/N
μ = (1.44+1.41+1.42+1.49+1.35+1.5+1.39+1.48+1.49+1.39+1.49+1.46+1.41++1.44+1.46)/15
μ = 21.57/15
μ = 1.44
b) What is the Median selling price?
Higher to lower Lower to higher
1.49 1.35
1.49 1.39
1.49 1.39
1.48 1.41
1.46 1.41
1.45 1.42
1.45 1.44
1.44 1.44 ⟷ Median1.44
1.44 1.45
1.42 1.45
1.41 1.46
1.41 1.48
1.39 1.49
1.39 1.49
1.35 1.49

c) What is the Model selling price?...