Complete the data set with one value so the mean of the data is 13 using numbers
10, 14, 8, 16, 12, x. X=18
Which value can you remove from new set of data so that mean is 14?
Right, x = 18
mean = ∑x/n
Therefore mean * N = ∑x
14 * 5 = 70
Which 5 scores will = 70?
To find the missing value x that would make the mean of the data set 13, we can use the formula for the mean:
Mean = (Sum of all values) / (Number of values)
Given the data set: 10, 14, 8, 16, 12, x
We can calculate the sum of all values in the data set by adding them together:
10 + 14 + 8 + 16 + 12 + x
To find the missing value, we can set up an equation using the mean formula:
13 = (Sum of all values + x) / (Number of values + 1)
We know that the sum of all values is 10 + 14 + 8 + 16 + 12, which equals 60. The number of values is 6.
13 = (60 + x) / (6 + 1)
To solve for x, we can multiply both sides of the equation by the denominator (6 + 1) to remove the fraction:
13 * (6 + 1) = 60 + x
91 = 60 + x
To isolate x, we subtract 60 from both sides of the equation:
91 - 60 = x
x = 31
Therefore, the missing value x that would make the mean of the data set 13 is 31.
Now, to find which value can be removed from the new set of data so that the mean is 14, we can calculate the sum of all values in the new set:
10 + 14 + 8 + 16 + 12 + 18
The sum of these values is 78. To find the value that can be removed, we can set up an equation using the mean formula:
14 = (78 - x) / (6 - 1)
To solve for x, we can multiply both sides of the equation by the denominator (6 - 1):
14 * (6 - 1) = 78 - x
70 = 78 - x
To isolate x, we subtract 78 from both sides of the equation:
70 - 78 = -x
x = -8
Therefore, the value that can be removed from the new set of data so that the mean is 14 is -8.
To complete the data set so that the mean of the data is 13, we need to find the missing value (x). The mean of a data set is found by summing all the values in the data set and dividing by the total number of values.
In this case, the given values are 10, 14, 8, 16, 12, and x (where x is the missing value). The sum of these values can be found by adding them together: 10 + 14 + 8 + 16 + 12 + x.
To make the mean 13, we need to have a total sum of 13 multiplied by the total number of values (which is 6 in this case). This gives us: 13 * 6 = 78.
Now we can set up an equation: 10 + 14 + 8 + 16 + 12 + x = 78.
Simplifying the equation, we have: 60 + x = 78.
Subtracting 60 from both sides of the equation, we find that x = 18.
Therefore, the missing value (x) is 18, and the completed data set with a mean of 13 would be:
10, 14, 8, 16, 12, 18.
Now, to find the value that can be removed from this new set of data so that the mean is 14, we need to calculate the sum of the values in the data set:
10 + 14 + 8 + 16 + 12 + 18 = 78.
Since the mean is the sum divided by the total number of values, we divide the sum by 6 (the total number of values) to find the mean: 78 / 6 = 13.
To have a mean of 14, the sum of the values should be 14 multiplied by the total number of values (which is still 6), giving us: 14 * 6 = 84.
To find the value that can be removed, we subtract the desired sum from the current sum: 84 - 78 = 6.
Therefore, the value that can be removed from the new set of data so that the mean is 14 is 6.