Statistics: How do I find the mean+median of this question?

C

callmeashleykk

New member
Joined
Feb 10, 2023
Messages
7
In one neighborhood there are 19 households with an annual income of $50,000 and one household with an annual income of $1,050,000. Describe in your own words whether the mean or median of these incomes is a better description of a typical household in the neighborhood.

How do I solve this?
 
Harry_the_cat said:
(a) What is the total income of all households?
(b) How many households are there?
(c) The mean is (a) divided by (b).
Click to expand...
For (a) do I do (50,000+1,050,000)= 1100000
(b) 19 households
(c) Mean: (1100000/19)= 57894.7368421

Is (a-c) correct? And how do I find the median I don't see a list of numbers that will make me find the median.
 
callmeashleykk said:
For (a) do I do (50,000+1,050,000)= 1100000
(b) 19 households
(c) Mean: (1100000/19)= 57894.7368421

Is (a-c) correct? And how do I find the median I don't see a list of numbers that will make me find the median.
Click to expand...
Not quite.
(a) There are 19 households with 50,000. Your calculation only considered 1 household.
(b) Again, there are 19 households with 50,000 and one with 1,050,000. So it should be 1+19 = 20.
 
BigBeachBanana said:
Not quite.
(a) There are 19 households with 50,000. Your calculation only considered 1 household.
(b) Again, there are 19 households with 50,000 and one with 1,050,000. So it should be 1+19 = 20.
Click to expand...
(a) (50,000+1,050,000)= 11,000,000
(b) 20 households
(c) Mean: (11,000,000/20)= 550,000
(d) Median: (100,000/2)= 50,000
These are the final answers I got which I think is correct now.

However I'm still stuck on how to "describe whether the mean or median of these incomes is a better description of a typical household in the neighborhood." in the problem.
 
If you need a list to find the median, write out $50,000 nineteen times and then $1,050,000 just once.
These are the 20 values you are dealing with.
 
callmeashleykk said:
In one neighborhood there are 19 households with an annual income of $50,000 and one household with an annual income of $1,050,000. Describe in your own words whether the mean or median of these incomes is a better description of a typical household in the neighborhood.

How do I solve this?
Click to expand...
Maybe it would help you to have look at this post, @callmeashleykk (it would do no harm to have a read through the whole of that thread too)? ?

Edit: One extra little bit of help. When you\need to find the Median when there is an even number of data points, there is no single number right in the middle (unlike in my example where there were fifteen numbers so the middle one had exactly seven before it and seven after it) so what you do (for example, in your case, where there are 20 pieces of data) is you take the two 'middle' values (the 10th & the 11th) and you calculate their mean value as the median, ie: you add them together and divide the answer by 2. If those two are the same then their mean will be the same too (obviously?), eg: 10+10=20 and 20÷2=10.
 
Last edited:
callmeashleykk said:
(a) (50,000+1,050,000)= 11,000,000
(b) 20 households
(c) Mean: (11,000,000/20)= 550,000
(d) Median: (100,000/2)= 50,000
These are the final answers I got which I think is correct now.

However I'm still stuck on how to "describe whether the mean or median of these incomes is a better description of a typical household in the neighborhood." in the problem.
Click to expand...
(a) It is still the same as before and it's not correct.
If each of the households brings in 50,000 then, how much do 19 households bring in?

(b) Correct

(c) It's incorrect because (a) is incorrect.

(d) The answer is correct but for the wrong reason.
To find the median, list the income in sequential order as such:

[math]50,000 \quad 50,000 \quad 50,000 \quad 50,000 \quad \dots \quad 1,050,000\\[/math]
What is the value that is in the middle of your list?

Can you fix your mean and median first, then we can discuss which is a better measure.
 
BigBeachBanana said:
(a) It is still the same as before and it's not correct.
If each of the households brings in 50,000 then, how much do 19 households bring in?

(b) Correct

(c) It's incorrect because (a) is incorrect.

(d) The answer is correct but for the wrong reason.
To find the median, list the income in sequential order as such:

[math]50,000 \quad 50,000 \quad 50,000 \quad 50,000 \quad \dots \quad 1,050,000\\[/math]
What is the value that is in the middle of your list?

Can you fix your mean and median first, then we can discuss which is a better measure.
Click to expand...
The Problem:
In one neighborhood there are 19 households with an annual income of $50,000 and one household with an annual income of $1,050,000. Describe in your own words whether the mean or median of these incomes is a better description of a typical household in the neighborhood.

(a) Total Income of the 19 households: (50,000*19)= 950,000
(b) All of the households: (1+19)= 20 households
(c) Mean: (950,000/20)= 47,500
(d) Median: Last 2 numbers in the middle were 50,000. (50,000+50,000=100,000) then (100,000/2=50,000) Median is 50,000.
(I wrote down 50,000 nineteen times and 1,050,000 one time at the end and started crossing each number off, till I got to the last middle digits to find the median and divided by 2.)

Hoping (a-d) are all correct now.


Mean: $47,500 Median: $50,000
"Describe in your own words whether the mean or median of these incomes is a better description of a typical household in the neighborhood."

(e) The median, $50,000 is the best income of a typical household since the mean is $47,500 which is less than how much the median is.
 
callmeashleykk said:
The Problem:
In one neighborhood there are 19 households with an annual income of $50,000 and one household with an annual income of $1,050,000. Describe in your own words whether the mean or median of these incomes is a better description of a typical household in the neighborhood.

(a) Total Income of the 19 households: (50,000*19)= 950,000
(b) All of the households: (1+19)= 20 households
(c) Mean: (950,000/20)= 47,500
(d) Median: Last 2 numbers in the middle were 50,000. (50,000+50,000=100,000) then (100,000/2=50,000) Median is 50,000.
(I wrote down 50,000 nineteen times and 1,050,000 one time at the end and started crossing each number off, till I got to the last middle digits to find the median and divided by 2.)

Hoping (a-d) are all correct now.


Mean: $47,500 Median: $50,000
"Describe in your own words whether the mean or median of these incomes is a better description of a typical household in the neighborhood."

(e) The median, $50,000 is the best income of a typical household since the mean is $47,500 which is less than how much the median is.
Click to expand...
Really close! I'll correct it for you.

(a) You have to consider the 1,050,000 households as well when computing the mean.

[imath](50,000 \times 19 + 1,050,000) = 2,000,000[/imath]

(c) Mean = [imath]\dfrac{2,000,000}{20} = 100,000[/imath]

Does the mean of 100,000 change your opinion about (e)?
 
OK, now that the correct values for the Median ($50,000) and the Mean ($100,000, ie: twice the median income) incomes have been (eventually) arrived at (did you read, carefully, the post I referred you to earlier?) which of those two statistics is a "better description of a typical household in the neighborhood"? (Bearing in mind that the vast majority (95%) of the households bring in $50,000 but there is one (very lucky!) household that enjoys an income that is a million dollars more than anyone else's! We call this an 'outlier' in Statistics.)
Remember: your answer should "Describe in your own words" whether (and why) the mean or median is the more appropriate statistic. (Remember, too, that in answering this question you would only get full credit if you showed correct calculation of the median & mean along with your assessment of their suitability to (approximately?) describe neighbourhood incomes. That is why it is important that you learn how to calculate these things correctly; I say again: read carefully through my previous post and also look at the website I recommended in it!)
 
Last edited:
BigBeachBanana said:
Really close! I'll correct it for you.

(a) You have to consider the 1,050,000 households as well when computing the mean.

[imath](50,000 \times 19 + 1,050,000) = 2,000,000[/imath]

(c) Mean = [imath]\dfrac{2,000,000}{20} = 100,000[/imath]

Does the mean of 100,000 change your opinion about (e)?
Click to expand...
The Problem:
In one neighborhood there are 19 households with an annual income of $50,000 and one household with an annual income of $1,050,000. Describe in your own words whether the mean or median of these incomes is a better description of a typical household in the neighborhood.

Thank you for helping me start off my problem @Harry_the_cat
Thank you for the corrections of (a-c) @BigBeachBanana
And thank you for the clarification for (e) @The Highlander (Yes, I have read the referred post!)

Mean: 100,000 Median: 50,000
(e) The mean is $100,000, and the median is $50,000 from these two outcomes the best option for a income of a typical household in the neighborhood is the mean with an income of $100,000.
 
callmeashleykk said:
Mean: 100,000 Median: 50,000
(e) The mean is $100,000, and the median is $50,000 from these two outcomes the best option for a income of a typical household in the neighborhood is the mean with an income of $100,000.
Click to expand...
Why do you say the mean is the better option for a typical household income?
You see most of your household income in your data set is 50,000. Does 100,000 accurate paint this picture?
 
BigBeachBanana said:
Why do you say the mean is the better option for a typical household income?
You see most of your household income in your data set is 50,000. Does 100,000 accurate paint this picture?
Click to expand...
The Problem:
In one neighborhood there are 19 households with an annual income of $50,000 and one household with an annual income of $1,050,000. Describe in your own words whether the mean or median of these incomes is a better description of a typical household in the neighborhood.

Mean: 100,000 Median: 50,000

I thought the highest amount of money was suppose to be the income. Was 50,000 (median) the accurate amount since there were 19 households with the same amount?
 
callmeashleykk said:
The Problem:
In one neighborhood there are 19 households with an annual income of $50,000 and one household with an annual income of $1,050,000. Describe in your own words whether the mean or median of these incomes is a better description of a typical household in the neighborhood.

Mean: 100,000 Median: 50,000

I thought the highest amount of money was suppose to be the income. Was 50,000 (median) the accurate amount since there were 19 households with the same amount?
Click to expand...
I think the key word is "typical".

If someone wanted to state an "average" that would be most impressive, they might choose the larger of the two numbers; but you were asked for a number that describes the typical household -- one that most of them are closer to.
 
The Problem:
In one neighborhood there are 19 households with an annual income of $50,000 and one household with an annual income of $1,050,000. Describe in your own words whether the mean or median of these incomes is a better description of a typical household in the neighborhood.

Mean: 100,000 Median: 50,000

(FIXED): The median is $50,000, and the mean is $100,000 from these two outcomes the best option for a income of a typical household in the neighborhood is the median with an income of $50,000.
 
You must log in or register to reply here.
Top