What is the range of this function?
1 answer:
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Given list of values
A = {23, 34, 19, 10, 9, 20, 40, 43, 28, 29, 36, 13, 27, 23, 36, 37, 7}
Sort list A to get list B
B = {7, 9, 10, 13, 19, 20, 23, 23, 27, 28, 29, 34, 36, 36, 37, 40, 43}
The smallest value is 7, so the min is 7
The largest value is 43, so the max is 43
Look through list B to find the middle-most value. What you can do is cross off each pair of outer values (see figure 1 in the attached images) until you are left with the middle value
Or you can note how there are 17 values so the median is at slot 9 (there are 8 values below the median; 8 values above the median; the 8 is from 17/2 = 8.5)
Once you know the median is 27, we split the list B into two parts
The first part, we'll call it L for lower half is
L = {7, 9, 10, 13, 19, 20, 23, 23}
which is the list of all values lower or smaller than the median.
The median of list L is 16 because its the midway point between 13 and 19. We can compute (13+19)/2 = 32/2 = 16. This is the value of Q1
The upper half U is
U = {28, 29, 34, 36, 36, 37, 40, 43}
this list shows all the values larger than the median.
The value of Q3 is 36. We find the midpoint of 36 and 36 which is just 36.
The value of Q3 is the same as the median of list U
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Five Number Summary:
Min = 7
Q1 = 16
Median = 27
Q3 = 36
Max = 43
This five number summary is then used to construct the box-and-whisker plot. See figure 2 in the attached images. The diagram shows how each piece of the boxplot is put together (eg: the left edge of the box is the value of Q1).
A = {23, 34, 19, 10, 9, 20, 40, 43, 28, 29, 36, 13, 27, 23, 36, 37, 7}
Sort list A to get list B
B = {7, 9, 10, 13, 19, 20, 23, 23, 27, 28, 29, 34, 36, 36, 37, 40, 43}
The smallest value is 7, so the min is 7
The largest value is 43, so the max is 43
Look through list B to find the middle-most value. What you can do is cross off each pair of outer values (see figure 1 in the attached images) until you are left with the middle value
Or you can note how there are 17 values so the median is at slot 9 (there are 8 values below the median; 8 values above the median; the 8 is from 17/2 = 8.5)
Once you know the median is 27, we split the list B into two parts
The first part, we'll call it L for lower half is
L = {7, 9, 10, 13, 19, 20, 23, 23}
which is the list of all values lower or smaller than the median.
The median of list L is 16 because its the midway point between 13 and 19. We can compute (13+19)/2 = 32/2 = 16. This is the value of Q1
The upper half U is
U = {28, 29, 34, 36, 36, 37, 40, 43}
this list shows all the values larger than the median.
The value of Q3 is 36. We find the midpoint of 36 and 36 which is just 36.
The value of Q3 is the same as the median of list U
------------------------------------------------
Five Number Summary:
Min = 7
Q1 = 16
Median = 27
Q3 = 36
Max = 43
This five number summary is then used to construct the box-and-whisker plot. See figure 2 in the attached images. The diagram shows how each piece of the boxplot is put together (eg: the left edge of the box is the value of Q1).
Answer: The team won 100 games and losses 28 games
Step-by-step explanation:
Let the number of games won denoted by x and the games lost is denoted by y .
Given : A minor league baseball team plays 128 games in a season.
Team won 16 more than three times as many games as they lost.
Then, the system of equations, we have
We can rewrite equation (2) as
Now, Eliminate equation (3) from (1), we get
Substitute the value of y in (2), we get
Hence, the team won 100 games and losses 28 games.
Answer: 208.
Step-by-step explanation:
The formula to find the minimum sample size is given by :-
(1)
, where z* = critical z-value (two tailed).
= Standard deviation ( from prior study ) and E = Margin of error.
As per given , we have
Margin of error : E= 0.29
Confidence level = 85%
Significance level =
Using z-table , the critical value (two -tailed)=
As per previous study , Variance =
Now, the required minimum sample size = [Substitute the values in formula (1)]
[ Round to the next integer]
Hence, the minimum number of third graders that must be included in a sample = 208.