[pop000]

In the picture you can see an Histogram of Distribution of grade, of students.

First question:i asked to find the frequent grade and this is my options:
A)30
B)40
C)80
D)85
E)30 AND 85
I think the answer is A because most of the student get this grade yes?

2nd question, I asked to find the upper decile of the distribution grade, and this is my options:
A)80.96
B)85
C)86
D)97.4
I did like this:i found the sum of the students is 260 so the upper decile is 26 students but from here I am not sure how to keep on.
So I need help.
Thanks.

[Unknown008]

1. I think you mean the mode, if so, then you're right.

2. You will have to use area.

From 90 to 100, you have 10 students. So, there are 16 students left in that decile that you need to get.

Now, you have a quite big number between 80 and 90, having 40 students, but you need only 16!

You need to find the area blue:



and you already have 10.

That long rectangle in the next column is what has an area of 16.

The length of one side of a square is

The height of the blue rectangle is

The width is w.

So,

Find w. And to get where the mark is (red arrow), remove that value of w from 90.

[pop000]

HI thank you for your answer but for the first question yes I mean mode but why is can be answer E 30 and 85?
Thanks again.

[pop000]

*can't

[Unknown008]

Oops, I was only looking at the area, but not the frequency. Yes, both 35 and 85 are the modes of the distribution.

[pop000]

OK thank you :)

[pop000]

The answer for the 2nd question is C?

Thank you.

[Unknown008]

It should be 88.4 (by calculation), but since there's no answer... C is the closest one.

One quick way to work is out is to know that you need 16 of 40 students in the class 80-90. Half of it is at 85. Since 16 is a little less than 20 (half of the number), the 'limit' where the blue rectangle is must be slightly to the right of 85, which gives 86.

[pop000]

OK thank you :)