  # At their​ inauguration, the ages of the first six​ (out of a current number of​ 45) presidents of a certain country were 55,64,61,65,64 and 53.Find the standard deviation of the ages at inauguration of the first six presidents.

Question

At their​ inauguration, the ages of the first six​ (out of a current number of​ 45) presidents of a certain country were 55,64,61,65,64 and 53.

Find the standard deviation of the ages at inauguration of the first six presidents.

check_circleExpert Solution
Step 1

First we will find the sample standard deviation the steps are as follows

1) Step 1: Find the mean of data set

we got the mean to be 60.3333

2) Step 2: Subtract the mean from every data point

for example : (55-60.3333) = -5.3333

(64-60.3333) = 3.67

and so on

3) Step 3: Whatever you get in step 2 square that

for example square of -5.333 is (-5.333*-5.333) = 28.4089

square of 3.67 is (3.67*3.67) = 13.4689

4) Step 4: Add the values of step 3

total of third column is 131.3334

5) Step 5: Whatever you get in step 4 divide that by (n - 1)

n is the number of data points in any data

n is 6 because we have 6 data points

6) Step 6: whatever you get in step 6 square root that and you get sample standard deviation.

we got 26.6668 by dividing with 5 and when we got its square root so we got 5.1251 so 5.1251 is our sample standard deviation

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