F5 math measures of dispersion

Question

1. Mary is one of the students in the class and her standard score in the test is 1.

Is Mary one of the top 20% students of the class in the test? Explain.

2. Picture of stem-and-leaf diagram:

http://postimg.org/image/x0mifgg65/

The librarian of the school ran a reading award scheme in the second term. The

following table shows some statistics of the distribution of the numbers of books

read by these 24 students in the second term.

Minimum:8

Lower quartile:26

Median:35

Upper quartile:41

Maximum:46

The librarian claims that not less than 50% of these students read at least 5 more

Books in the second term than that in the first term. Do you agree? Explain your

answer.

Please help, thank you!

Answer 1

最愛解答

1.

If the test score follows a normal distribution, then YES.

This is because for a normal distribution, 68% of the population falls within plus and minus 1 standard deviation from the mean.

That means, there is only (1 - 68%)/2 = 16% of the population which has a test score one standard deviation above the mean.

Mary has a standard score of 1, that is, her test score is exactly one standard deviation above the mean. She is just at the top 16%, so she is one of the top 20% students of the class.

圖片參考：https://s.yimg.com/lo/api/res/1.2/xRXzHJQDTFeozBfc...

2.

圖片參考：https://s.yimg.com/rk/HA00430218/o/1916976708.jpg

The librarian's claim is AGREED.

The old maximum is 30.

That means, all students read no more than 30 books.

The new median is 35.

That means, at least half of the students read 35 or more books.

These at least half of the students read no more than 30 books in the first term but read 35 or more books in the second term.

Therefore, these at least half of the students read at least 5 more books in the second term than that in the first term.