Question

A center for education statistics reported average mathematics achievement scores for eighth graders in 22 nations. The average scores for each nation are given below. 227 337 352 356 364 374 388 409 449 471 480 483 484 495 500 504 505 525 532 548 581 600 ?a) Find the? 5-number summary, the? IQR, the? mean, and the standard deviation of these national averages.

Answer 1

In this problem, we need to find

Minimum, Maximum, first quartile, Third quartile, Median, Mean and Standard deviation

first we arrange the data in ascending order

Ascending order : 227 337 352 356 364 374 388 409 449 471 480 483 484 495 500 504 505 525 532 548 581 600

Minimum value = 227

Maximum value = 600

First quartile = (n + 1) / 4 = (22 + 1) / 4 = 5.75th term

Approximately, 6th term = 374

Third quartile = 3(n + 1) / 4 = 3(22 + 1) / 4 = 17.25th term

Approximately 17th term = 505

Median = (480 + 483) / 2 = 481.5

Now five number summary

(Min, First quartile, Median, Third quartile and Maximum)

= (227, 374, 481.5, 505, 600)

Mean = (227 + 337 + ...........+ 600) / 22 = 452.91

Standard deviation = [(227 - 452.91)² + (337 - 452.91)² + ..............+ (600 - 452.91)² / 22-1

= 91.32