A list of 11 positive integers has a mean of 10, a median of 9, and a unique mode of 8. What is the
Poftethef9t
Answered question
2022-06-06
From the information, I got the following information:
11 integers with a mean of 10 means a total must be 110.
A unique mode means that there must be at least two 8's.
if there are two 8's, and the median is 9, there must be at least two numbers greater than 9 also.
Answer & Explanation
Ethen Valentine
Beginner2022-06-07Added 15 answers
We want to make as large as possible, while keeping everything else positive, and making sure is the unique mode. This means making the sum of through as small as possible, while respecting the same constraints.
As a first case, we try using exactly two 's, so every other number can only occur once. This gives us:
or
As a second case, let's try three 's, which allows us to use each other number twice:
or
That seemed to help, so let's try four 's:
or
Finally, with five 's, we have:
or
This exhausts the cases.
vrotterigzl
Beginner2022-06-08Added 3 answers
A simpler point is that you know from the median that there are no more than five numbers strictly below 9 and no more than five numbers strictly above 9. It would be helpful if the five smallest could be as small as possible within the constraints so as to make the biggest in the whole set as large as possible. You also want four of the five largest to be as small as possible. So, subject to the constraints, consider
if five of the five smallest are 8s then you could have
8,8,8,8,8,9,9,9,9,10,24
if four of the five smallest are 8s then you could have
1,8,8,8,8,9,9,9,10,10,30
if three of the five smallest are 8s then you could have
1,1,8,8,8,9,9,10,10,11,35
if two of the five smallest are 8s then you could have
1,2,3,8,8,9,10,11,12,13,33
and choose the pattern with the largest maximum.
New Questions in Descriptive Statistics
What is the range of the function ?
The domain and range of is
A)
B)
C)
D)Mean of the squares of the deviations from mean is called the:
Variance
Standard deviation
Quartile deviation
ModeHow to evaluate P(10,2)?
What is the effect of wind speed on evaporation?
What is the range of a linear function?
Find the range of
State the main limitations of statistics.
What is the range of the function y = x?
Tell whether the statement is true or false : A data always has a mode.
In most cases,_____variables are not considered to be equal unless they are exactly the same.
A local newspaper in a large city wants to assess support for the construction of a highway bypass around the central business district to reduce downtown traffic. They survey a random sample of 1152 residents and find that 543 of them support the bypass. Construct and interpret a 95% confidence interval to estimate the proportion of residents who support construction of the bypass.
What is the right answer and how?
Define lateral displacement.
