Answer to Question #187857 in Statistics and Probability for Shan

Question

find the estimate for the mean the variance and the standard deviation of the salaries of all the professors in all schools at the university belt area

Answer 1

Since in this problem , data is not given

So,

 Estimate the Mean:

The method for estimating the mean can be outlined as follows:

Step 1. Add a new column to the table writing down the midpoint (middle value) of each group.

Step 2. Multiply each midpoint by the frequency of that group and add the results in a new column..

Step 3. Add the values in the midpoint × frequency column.

Step 4. Divide that value by the total frequency to get the estimate of the mean.

For the Standard Deviation:

Use this step-by-step approach to find the standard deviation for a discrete variable.

Calculate the mean.

1. Subtract the mean from each observation.
2. Square each of the resulting observations.
3. Add these squared results together.
4. Divide this total by the number of observations (variance, S²).
5. Use the positive square root (standard deviation, S).

The standard deviation for a discrete variable made up of n observations is the positive square root of the variance and is defined as:

$$S=\sqrt{\dfrac{\sum(x-\bar x)^2}{n}}$$

For the Variance:

Calculating variance involves squaring deviations, so it does not have the same unit of measurement as the original observations.

The variance for a discrete variable made up of n observations is defined as:

$$S^2=\dfrac{\sum(x-\bar x)^2}{n}$$