The Los Angeles Times regularly reports the air quality inde

The Los Angeles Times regularly reports the air quality index for various areas of Southern California. A lower index value means better or cleaner air. A sample of air quality index values for Pomona provided the following data: 23, 37, 53, 43, 40, 50, 55, 44, and 45.

Compute the range and interquartile range.

Compute the sample mean, sample variance, and sample standard deviation (to 2 decimals).

A sample of air quality index readings for Anaheim provided a sample mean of 48.3, 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?

Solution

The Los Angeles Times regularly reports the air quality index for various areas of Southern California. A lower index value means better or cleaner air. A sample of air quality index values for Pomona provided the following data: 23, 37, 53, 43, 40, 50, 55, 44, and 45.

Compute the range and interquartile range.

Sorted data

23

37

40

43

44

45

50

53

55

Range = 55-23=32

Interquartile range

Q1=40

Q3=50

Interquartile range = 50-40=10

Compute the sample mean, sample variance, and sample standard deviation (to 2 decimals).

Sample mean = 390/9=43.33

Sample variance = (17642-390²/9)/8 =

92.75

Sample standard deviation = sqrt( 92.75) = 9.63

A sample of air quality index readings for Anaheim provided a sample mean of 48.3, 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?

Mean , variance and standard deviation of air quality Index of Pomona are less than Anaheim.

We conclude that Pomona is better or cleaner air than Anaheim