Number of goals : 0, 1,2,3,4,5
Number of matches : 7,x,5,3,1,4
(a) if the mean number is more than 2, find the largest possible value of x.
(b) if the median number of goals is 2, find the largest possible value of x
Total # of matches: 7+x+5+3+1+4 = 20 + x
Total # of goals: 1*x + 5*2 + 3*3 + 1*4 + 4*5 = 43 + x
If x = 0, the mean per game is 43/20 = 2.15
If x = 1, mean = 2.095
If x = 2, mean = 2.045
if x = 3, mean = 2.000
The answer to a is x=2
The answer to b is x=3
I agree with drwls
THANKS ! :D
To find the largest possible value of x in each scenario, we need to understand the conditions for mean and median.
(a) Condition for Mean:
Mean = sum of all numbers / total number of numbers
To find the largest possible value of x when the mean is more than 2, we need to calculate the sum of all numbers and the total number of numbers.
Given data:
Number of goals: 0, 1, 2, 3, 4, 5
Number of matches: 7, x, 5, 3, 1, 4
Using the given data, we can calculate the sum of all numbers:
Sum = 0 + 1 + 2 + 3 + 4 + 5 = 15
We also know the total number of numbers is 6.
Now, we can set up an equation to find the largest possible value of x:
Mean = 2
Sum / Total number of numbers = 2
15 / 6 = 2.5
Since the mean (2.5) is more than 2, we need to find a value of x that makes the mean less than or equal to 2.
Let's assume x is the largest possible value. We will substitute this value in the equation and solve for x:
(15 + x) / (6 + 1) ≤ 2
(15 + x) / 7 ≤ 2
15 + x ≤ 14
x ≤ 14 - 15
x ≤ -1
Therefore, the largest possible value of x is -1.
(b) Condition for Median:
The median is the middle value when the numbers are arranged in ascending or descending order.
To find the largest possible value of x when the median is 2, we need to rearrange the numbers in ascending order.
Given data:
Number of goals: 0, 1, 2, 3, 4, 5
Number of matches: 7, x, 5, 3, 1, 4
Rearranging the number of goals in ascending order, we have: 0, 1, 2, 3, 4, 5
Since the median is 2, the middle value is 2. We can see that x can be any value between 1 and 3 to maintain the median as 2.
Therefore, the largest possible value of x is 3.