The mean of the numbers 3, 6,
4, x and 7 is 5. Find the standard
deviation
A. √2
B. √3
C. 2
D. 3
To find the standard deviation, we first need to find the variance.
The mean of the numbers given is 5, so we can find the sum of the numbers:
3 + 6 + 4 + x + 7 = 5(5)
20 + x = 25
x = 5
Substituting x = 5, the sum of the numbers is 25.
Next, we can find the sum of the squares of the differences between each number and the mean:
(3 - 5)^2 + (6 - 5)^2 + (4 - 5)^2 + (5 - 5)^2 + (7 - 5)^2
+ (-2)^2 + 1^2 + (-1)^2 + 0^2 + 2^2
+ 4 + 1 + 1 + 0 + 4
= 10
The variance is the average of these squared differences:
10/5 = 2
Finally, the standard deviation is equal to the square root of the variance:
√2
So, the answer is A. √2.
To find the standard deviation, we need to find the variance first.
Step 1: Calculate the mean (average) of the given numbers.
Mean = (3 + 6 + 4 + x + 7)/5 = (20 + x)/5 = 5
Step 2: Solve for x in the equation (20 + x)/5 = 5.
20 + x = 25
x = 5
Now we can calculate the variance.
Step 3: Calculate the squared difference between each number and the mean.
(3 - 5)^2 + (6 - 5)^2 + (4 - 5)^2 + (5 - 5)^2 + (7 - 5)^2
= 4 + 1 + 1 + 0 + 4
= 10
Step 4: Divide the sum from step 3 by the total number of data points.
Variance = 10/5 = 2
Finally, we can calculate the standard deviation.
Step 5: Take the square root of the variance.
Standard Deviation = √(2) = √2
Therefore, the correct answer is A. √2.