The National Association of College and University Business Officers collects data on college endowments. In 2015, its report included the endowment values of 841841 colleges and universities in the United States and Canada. When the endowment values are arranged in order, what are the locations of the median and the quartiles in this ordered list

Question

12-02-2021
Mathematics

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The National Association of College and University Business Officers collects data on college endowments. In 2015, its report included the endowment values of 841841 colleges and universities in the United States and Canada. When the endowment values are arranged in order, what are the locations of the median and the quartiles in this ordered list

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MrRoyal MrRoyal · Answer 1 · 2021-02-13T04:51:27+01:00

Answer:

[tex]M = 421[/tex]

[tex]Q_1 = 210.5[/tex]

[tex]Q_3 = 631.5[/tex]

Step-by-step explanation:

Given

[tex]N = 841[/tex] --- Number of colleges

Required

Determine the location of the median and the quartiles

For the median (M), the location is calculated using:

[tex]M = \frac{1}{2}(N+1)[/tex]

Substitute 841 for N

[tex]M = \frac{1}{2}(841+1)[/tex]

[tex]M = \frac{1}{2}(842)[/tex]

Remove bracket

[tex]M = \frac{1}{2}*842[/tex]

[tex]M = 421[/tex]

For the lower quartile (Q1), the location is calculated using:

[tex]Q_1 = \frac{1}{4}(N+1)[/tex]

Substitute 841 for N

[tex]Q_1 = \frac{1}{4}(841+1)[/tex]

[tex]Q_1 = \frac{1}{4}(842)[/tex]

Remove bracket

[tex]Q_1 = \frac{1}{4}*842[/tex]

[tex]Q_1 = 210.5[/tex]

Since the positions are whole numbers, you simply calculate the average of the 211st and the 212nd entry

For the upper quartile (Q3), the location is calculated using:

[tex]Q_3 = \frac{3}{4}(N+1)[/tex]

Substitute 841 for N

[tex]Q_3 = \frac{3}{4}(841+1)[/tex]

[tex]Q_3 = \frac{3}{4}(842)[/tex]

Remove bracket

[tex]Q_3 = \frac{3}{4}*842[/tex]

[tex]Q_3 = 631.5[/tex]

Since the positions are whole numbers, you simply calculate the average of the 631st and the 632nd entry