Question

The New York Times regularly reports the air quality index for various areas of New York. A sample of air quality index values for Harlem provided the following data: 32, 28, 26, 35, 43, 62, 57, 49, and 67.

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 Queens provided a sample mean of 43.5, a sample variance of 126, and a sample standard deviation of 9.46. What comparisons can you make between the air quality in Harlem and that in Queens on the basis of these descriptive statistics?

Answer 1

Following table shows the ordered data set and calculations for mean and variance:

	X	(x-mean)^2
	26	335.9889
	28	266.6689
	32	152.0289
	35	87.0489
	43	1.7689
	49	21.8089
	57	160.5289
	62	312.2289
	67	513.9289
Total	399	1852.0001

(a)

The range is:

Range: Maximum - Minimum = 67-26 = 41

First quartile:

Since there are 9 data values in the data set and first half of data set has 5 data values so first quartile will be 3rd data value. So,

Third quartile:

Since there are 9 data values in the data set and second half of data set has 5 data values so third quartile will be 7th data value. So,

?

The interquartile is:

b)

The sample mean is:

The sample variance is:

The sample standard deviation is;

c)

The sample variance is greater for air quality index values for Harlem in comparison to Queens so it seems that  the air quality in Queens is more consistent.