Question

Magdeline wants to know if the number of words on a page in her art book is generally more than the number of words on a page in her science book. She takes a random sample of 25 pages in each book and then calculates the mean, median, and mean absolute deviation for the 25 samples of each book.

Book
Mean
Median
Mean Absolute Deviation
Art
68.7
50
15.4
Science
54.2
55
7.9

She claims that because the mean number of words on each page in the art book is greater than the mean number of words on each page in the science book, the art book has more words per page. Based on the data, is this a valid inference?

Yes, because the mean is larger in the art book
No, because the mean is larger in the art book
Yes, because there is a lot of variability in the art book data
No, because there is a lot of variability in the art book data

Answer 1

I can't tell what the numbers are for your table, can you make them clearer. Otherwise here you will have to perform a Two Sample T test for the means. That would be the most accurate way of getting the solution.

Answer 2

I do I put the table up there.

Answer 3

yeah but I can't tell which values correspond to which

Answer 4

ah, I suppose they are all in order.

Answer 5

It should be option C, although you can also copmlete a two-sample T test.

Answer 6

I have one more question.

Answer 7

Carlton is using the following data samples to make a claim about the house values in his neighborhood:

House
Value
A
$100,000
B
$600,000
C
$650,000
D
$700,000
E
$900,000


Based on the data, should Carlton use the mean or the median to make an inference about the house values in his neighborhood?

He should use the median because there is an outlier that affects the mean.
He should use the mean because there are no outliers that affect the mean.
He should use the mean because it is in the center of the data.
He should use the median because it is in the center of the data.

Answer 8

Actually to the previous question let me quickly complete a 2-sample T test to ensure it's correct. a moment please.

Answer 9

ok.

Answer 10

The previous one is actually option D.

Answer 11

Mean should be used for normal distributions with no major skew or distributions that are approved by the Central Limit Theorem.

Median should be used for skewed data.

That means that C and D are eliminated. Now we must calculate for outliers mathematically.
U<Q1-1.5IQR

V>Q3+1.5IQR

After calculations we get
U<-47500
V<162500

So there are no outliers in the data set. Although n≤30, we can still use the CLT as there is no major skew or outliers. This means we can use a mean option B

Answer 12

Thank you.

Answer 13

@Ferredoxin4, careful to guide and involve the user through the problem solving process and avoid giving any answers. Consider this your first warning.