Respuesta :
Answer: For California: μ = 33.1; σ² = 1120.50; Range = 32;
For Iowa: μ = 24.5; σ² = 32.73; Range = 19
Step-by-step explanation:
Mean is the average of a population or a sample. It is defined as
μ = ∑x / n, where
x is each number of the set;
n is the total individuals in the sample.
Calculating the Mean for sample of taste of pizza in California:
μ₁ = [tex]\frac{34+39+40+46+33+31+34+14+15+45}{10}[/tex] = 33.1
Calculating the Mean for the sample in Iowa:
μ₂ = [tex]\frac{28+25+35+16+25+29+24+26+17+20}{10}[/tex] = 24.5
Variance measures how far the number in the set is from the mean. Its formula is
σ² = (∑x-μ)² / n -1
which means to find the variance, you have to get the difference between the number and the mean, square the result, add all of them and then divide by (n-1) individuals.
The Variance for the sample in California is
σ² = [tex]\frac{(34 - 33.1)^{2}+(39-33.1)^{2}+(40-33.1)^{2}+(46-33.1)^{2}+(33-33.1)^{2}+(34-33.1)^{2}+(14-33.1)^{2}+(15-33.1)^{2}+(45-33.1)^{2}}{9}[/tex]σ² = 120.50
The Variance for the sample in Iowa is
σ² = 32.73
Range is the difference between the highest and the lowest number of the set: range = highest - lowest
For the sample in California, the Range is
range = 46 - 14 = 32
For the sample in Iowa:
range = 35 - 16 = 19
For California:
- Mean = 33.1;
- Variance = 120.50;
- Range = 32;
For Iowa:
- Mean = 24.5;
- Variance = 32.73;
- Range = 19;
