Answered

Discover how IDNLearn.com can help you learn and grow with its extensive Q&A platform. Find in-depth and accurate answers to all your questions from our knowledgeable and dedicated community members.

The Los Angeles Times regularly reports the air quality index for various areas of Southern
California. A sample of air quality index values for Pomona provided the following
data: 28, 42, 58, 48, 45, 55, 60, 49, and 50.
a. Compute the range and interquartile range.
b. Compute the sample variance and sample standard deviation.
c. A sample of air quality index readings for Anaheim provided a sample mean of 48.5,a sample variance of 136, and a sample standard deviation of 11.66. What comparisons can you make between the air quality in Pomona and that in Anaheim on the basis of these descriptive statistics?

Sagot :

Fichohidn

Answer:

Range = 32 ; IQR = 13 ; Variance = 92.75 ; Standard deviation = 9.63

Step-by-step explanation:

Given the data:

28, 42, 58, 48, 45, 55, 60, 49, 50

Reorderd data: 28, 42, 45, 48, 49, 50, 55, 58, 60

The range: maximum - minimum

Range = 60 - 28 = 32

Interquartile range (IQR) : Q3 - Q1

Q3 = 3/4(n+1) th term. ; n = sample size

Q1 = 1/4(n+1)th term.

Using calculator :

Q3 = 56.5 ; Q1 = 43.5

IQR = 56.5 - 43.5 = 13

The variance :

Σ(X - m)^2 / n-1

m = Σx / n

Mean, m = 435 / 9 = 48.33

Variance :

[(28-48.33)^2 + (42-48.33)^2 + (45-48.33)^2 + (48-48.33)^2 + (49-48.33)^2 + (50-48.33)^2 + (55-48.33)^2 + (58-48.33)^2 + (60-48.33)^2] / 8

= 742.0001 / 8

= 92.75

Standard deviation = sqrt(Variance):

Sqrt(92.75) = 9.63

C.)

Sample mean are very close with a slightly greater Variability in the air quality of Anaheim over Pomona

We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Discover the answers you need at IDNLearn.com. Thank you for visiting, and we hope to see you again for more solutions.