Consider the rates of children (under 18 years of age) living in New York with grandparents as their primary caretakers. A sample of 13 New York count

Burhan Hopper 2021-02-24 Answered
Consider the rates of children (under 18 years of age) living in New York with grandparents as their primary caretakers. A sample of 13 New York counties yielded the following percentages of children under 18 living with grandparents.
5.9, 4.0, 5.7, 5.1, 4.1, 4.4, 6.5, 4.4, 5.8, 5.1, 6.1, 4.5, 4.9
a) Obtain and interpret the quartiles.
b) Determine and interpret the interquartile range.
c) Find and interpret the five-number summary
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Expert Answer

Brighton
Answered 2021-02-25 Author has 103 answers
Given data arranged in ascending order
4.0, 4.1, 4.4, 4.4, 4.5, 4.9, 5.1, 5.1, 5.7, 5.8, 5.9, 6.1, 6.5
First quartile, second quartile (median) and third quartile divide the data distribution into four equal halves. The median or second quartile is middle value.
As there are total 13 data points, median will be 7th data point.
Median = 5.1
The first quartile divide the first 25% of data distribution from rest 75%. As there are 13 data points, the first quartile will be 4th data point. First quartile = 4.4
The third quartile divide the first 75% of data distribution from rest 25%. As there are 13 data points, the first quartile will be 9th data point. Third quartile = 5.8
2) Interquartile range = Third quartile - First quartile
IQR=Q_3-Q_1=5.8-4.4=1.4
Interquartile range = 1.4
The interquartile range is a measurement of variability, it is the difference between the largest and lowest data points of middle 50% of the data.
3) The five number summary are lowest value, Quartile-1, Median, Quartile-3, Highest value
Lowest value = 4.0
Quartile -1 = 4.4
Median = 5.1
Quartile - 3 = 5.8
highest value = 6.5
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