In an article \"Grandchildren Raised by Grandparents, a Troubled Trend\" M. Blac

Question

In an article "Grandchildren Raised by Grandparents, a Troubled Trend" M. Blackburn considered the rates of children (under 18 years of age) living in California with grandparents as their primay care takers. A sample of 15 California counties yielded the following percentages of children under 18 living with grandparents.

5.5, 4.2 , 5.7, 5, 2.3, 4.4, 6.7, 6

4.4, 5.8, 5.1, 6.1, 4.4, 4.9, 4.8

Obtain and interpret the quartiles

Determine and interpret the interquartile range

Find and interpret the five-number summary

Identify potential outliers, if any

Explanation / Answer

First write given observations in ascending order.

2.3, 4.2 , 4.4 , 4.4 , 4.4, 4.8, 4.9, 5 , 5.1 , 5.5 , 5.7 , 5.8, 6 , 6.1 , 6.7

Five number summery is

1) minimum 2) first quartile 3) median 4) third quartile 5) maximum

1) minimum = 2.3

2) First quartile Q1 = n + 1 / 4th observation = 4th observation = 4.4.

3) median = n+1 / 2 th observation = 8 th observation = 5

4) third quartile Q3= 3n+1/ 4th observation= 11.5th observation = 5.75

5) Maximum= 6.7.

Interquartile range = Q3 - Q1

= 5.75 - 4.4

= 1.35

Outliers exists if a number is less than Q1 - 1.5×IQR or greater than Q3 + 1.5×IQR.

Q1 - 1.5×IQR = 2.375

So 2.3 is an outlier.

Q3 + 1.5×IQR. = 7.9

There is no upper outlier exists.

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