Question

mean and the standard deviation of 25 observations are 60 and 3 respectively later on it was decided to Om it and derivation which was correctly recorded as 50 calculate the mean and standard deviation of remaining 24 observations ​

Answer 1

Answer:

Please Mark this brainliest answer

Answer 2

Given,

• The mean of 25 observations is 60.

• The standard deviation of 25 observations is 3.

To find,

The mean and standard deviation after one observation of 50 is removed.

Solution,

The formula for mean is ∑$\frac{x_{i} }{n}$ where n is the number of observations.

The formula for standard deviation is $\sqrt{ \frac{x_{i}^{2} }{n} - X^{2}$ where X is the mean.

Now, as one observation is omitted,

Sum of all observation = Mean*number of observations = 1500.

Removing the observation of 50, new sum = 1500 - 50 = 1450.

The total number of observations now is 24.

New mean = $\frac{1450}{24} = 60.41$

Similarly, we find the new sum of the square of observations.

Standard deviation = $\sqrt{ \frac{x_{i}^{2} }{n} - X^{2}$

                            $3^{2} =$  $\frac{x_{i}^{2} }{n} - X^{2}$

                            $9*25 = x_{i}^{2} - 25*60*60\\90225 = x_{i}^{2}$

Removing the square of 50 from the sum of squares = 90225 - 2500

                                                                                         = 87725

New standard deviation = $\sqrt{ \frac{87725}{24} - 60.41^{2}$

                                         = $= \sqrt{ 3655.20 - 3649.36} \\= \sqrt{5.831}\\= 2.414$

Therefore, the new standard deviation is 2.414, and the new mean is 60.41.