Finding the median in a bar graph problem

[chwala]

Homework Statement

consider the attached graph. Answer the questions that follow.

Relevant Equations

bar graph

i do not understand the language used in part a, otherwise i would indicate the number of children the women have in order as $1,2,3,4,5$ and $6$
now for part b) this is where i have a problem. To find the median assumably for the number of children, we have to find the total number of children which is $108$, divide that by $2$ we get 54th item as our median which equates to $4$ is this correct?
now for part c) i do not understand the statement, or rather what they want...

 

[FactChecker]

This is a sample of women and the value of each data sample is the number of children that woman has.
b) To find the median, find the woman with half the women having fewer children. Then determine how many children she had.
c) To determine the mode, look for the value (of children) with the most women. That is the mode.

 

[phyzguy]

For part a, I don't know exactly what they are asking for either, but I think they want you to write down the number of children each woman has, with one entry for each woman. So this would be 1,1,1,1,1,2,2,2...
For part b, no you didn't do this correctly. You should take the total number of women, not the total number of children. How many women are in the sample?
For part c, do you know what the mode is? If not, you should be able to look this up.

 

[chwala]

so the median is in reference to the women and not children? the total number of women is $36$ implying that the median value will be the 18th item which equates to $7$ is this correct?

 

[phyzguy]

Yes. The question is asking for the median number of chidren a woman in the sample has.

 

[chwala]

and the mode therefore is $12$ right

 

[phyzguy]

so the median is in reference to the women and not children? the total number of women is $36$ implying that the median value will be the 18th item which equates to $7$ is this correct?

No! Try completing part a correctly. Then count to the 18th entry in your list.

 

[chwala]

No! Try completing part a correctly. Then count to the 18th entry in your list.

am not getting what you are saying...the women are $36$, or am i missing something?

 

[FactChecker]

so the median is in reference to the women and not children? the total number of women is $36$ implying that the median value will be the 18th item which equates to $7$ is this correct?

To find the median, find the woman where half the women have fewer children and half the women have more children. The median is the number of children that she has. It would be the 18th sample (woman) when put in order of the number of children that they have. How many children does the 18th sample have? (There are no women with 7 children, so that is wrong.)

 

[phyzguy]

and the mode therefore is $12$ right

No. The mode is the value of children that the most women have. No woman has 12 children so how could that be the mode?

am not getting what you are saying...the women are $36$, or am i missing something?

Yes, you are missing something. Again, start with answering question a corectly, as I told you earlier.

 

[chwala]

the language of the question is confusing to me lol, ok then the median will be $3$ and the mode will be$2$ correct?

 

[Office_Shredder]

That is right.

 

[phyzguy]

the language of the question is confusing to me lol, ok then the median will be $3$ and the mode will be$2$ correct?

Yes! Good. Bar graphs like this are confusing at first, but I think you get it now.

 

[chwala]

Yes! Good. Bar graphs like this are confusing at first, but I think you get it now.

Thanks phyzguy, now for part c) is the median the same as the mode...what does the statement mean? the answer would be no, i guess following from part b, right?

 

[phyzguy]

Well, if the median is 3 and the mode is 2, as you said, then they are not the same, right?

 

[chwala]

Well, if the median is 3 and the mode is 2, as you said, then they are not the same, right?

cheers ...

 

[andrewkirk]

@chwala I think what they are asking you to do in (a) is to write down for each woman in the club, the number of children she has. So they want you to write down 36 numbers, sorted from lowest to highest. From the graph you can see that first you need to write down five 1s, then twelve 2s, and so on.

Then, to find the median, you just take the average of the 18th and 19th numbers in that list.

You don't need to do all that to find the median, is the answer to (b). But I think they want you to do it that way rather than via a short cut, to reinforce the meaning of median. That's why they ask you to do (a) as well as (b).

 

[chwala]

@chwala I think what they are asking you to do in (a) is to write down for each woman in the club, the number of children she has. So they want you to write down 36 numbers, sorted from lowest to highest. From the graph you can see that first you need to write down five 1s, then twelve 2s, and so on.

Then, to find the median, you just take the average of the 18th and 19th numbers in that list.

You don't need to do all that to find the median, is the answer to (b). But I think they want you to do it that way rather than via a short cut, to reinforce the meaning of median. That's why they ask you to do (a) as well as (b).

Thanks mate...its now clear to me ...cheers.