The National Association of College and University Business Officers collects da

Question

The National Association of College and University Business Officers collects data on college endowments. In 2013, 849 colleges and universities reported the value of their endowments. When the endowment values are arranged in order, what are the locations of the median and the quartiles in this ordered list? Note, use half integers to represent results in between actual positions. Be sure you calculate your results manually exactly as described in the text and not using software which may have slightly different definitions for the median and quartiles.

Explanation / Answer

The data is arranged in ascending order.

Total number of data points = N = 849

(i) Median = 1/2 (N+1)th item.

i.e.,

1/2 (849 + 1)th item

i.e.,

425th item

(ii) First Quartile: Q1 is the (N+1)/4 th item

i.e.,

(849 + 1)/4th item

i.e.,

212.5th item.

i.e.,

average of 212th item & 213th item.

(iii) Third Quarlile: Q3 is the 3 (N+1)/4th item.

i.e.,

3 X 849/4th item

i.e.,

636.75th item.

i.e.,

Interpolation between 636th item & 637th item/

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