Question

Ten young adults living in California rated the taste of a newly developed sushi pizza topped with tuna, rice, and kelp on a scale of 1 to 50, with 1 indicating they did not like the taste and 50 that they did. The ratings were: 34 39 40 46 33 31 34 14 15 45 In a parallel study, 10 young adults in Iowa rated the taste of the same pizza. The ratings were: 28 25 35 16 25 29 24 26 17 20 Click here for the Excel Data File Calculate the range, mean and variance. (Round "mean" to 1 decimal place and "variance" to 2 decimal places.)

Answer 1

Answer: For California: μ = 33.1; σ² = 1120.50; Range = 32;

For Iowa: μ = 24.5; σ² = 32.73; Range = 19

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 =
`(34+39+40+46+33+31+34+14+15+45)/(10)` = 33.1

Calculating the Mean for the sample in Iowa:

μ₂ =
`(28+25+35+16+25+29+24+26+17+20)/(10)` = 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 =
`((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)`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;