A center for education statistics reported average mathematics achievement score

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 203 341 356 374 427 430 434 445 454 459 470 474 489 490 503 506 511 518 530 533 539 5575 a) Find the 5-number summary, the lQR, the mean, and the standard deviation of these national averages. The 5-number summary is O and O (Use ascending order. Type exact answers.) The IQR of the distribution is Type an exact answer.) The mean of the distribution is L. Round to one decimal place as needed.) The standard deviation of the distribution is (Round to one decimal place as needed.) b) Determine if the distribution of scores is symmetric or skewed and describe the middle 50% of the scores ls the distribution of average math achievement scores symmetric or skewed? O A. The distribution is symmetric, because the mean and median are approximately equal and the quartiles are approximately the same distance from the mean O B. The distribution is skewed, because the mean and median are not approximately equal. O C. The distribution is symmetric, because the mean and median are not approximately equal

Explanation / Answer

Ans:5-number summary

Minimum=203,First quartile=430,Median=472,Third quartile=511,Maximum=575

IQR=Third quartile-first quartile=511-430=81

Sorted Data Set: 575, 539, 533, 530, 518, 511, 506, 503, 490, 489, 474, 470, 459, 454, 445, 434, 430, 427, 374, 356, 341, 203

b)Option A is correct.(Distribution is symmetric)

middle 30% score fall between 430 and 511

c)25%

d)75%

Mean: 457.31818181818 Median: 472 Range: 372 Mode: All values appeared just once. Largest: 575 Smallest: 203 Sum: 10061 Count: 22

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