Mean Divided by Standard Deviation

Statistics is defined as a tool that is used to analyze the data. The data should be either numeric in origin or transformed from other form into numbers. Statistics is used to measure the average, middle most value, repeated values, variance and also find the standard deviations in the given data set. Statistics consists of the study about mean, median, mode, standard deviation, variance, range, etc. Study about mean divided by standard deviation with example problems.                  

I like to share this What is Standard Notation with you all through my article. 

Mean and standard deviation:

The illustrations of mean and standard deviadion is explained below individually as follows,

Mean: Finding the average is called as mean. For that divide the sum of  all the given values by total number of values given.

        Formula for finding the mean,

                                       `barx =` `(sum(x)) / n`

Standard Deviation: Take the square root for variance. Where variance is the ratio of the sum of square of deviations  from mean to one less than the number of data given.

                           

      S =   `sqrt((sum(x-barx)^2)/ (n-1))`

Mean divided by standard deviation:     `(barx)/ s`

where,

`barx ` = mean

s= standard deviation

Example problem of mean divided by standard deviation:

Mean divided standard Deviation - Problem1:
Calculate the mean divided standard deviation in the following data set.60, 64, 68, 69, 70.
Solution:
         To find the Mean:
                 Formula For finding the mean.
                                          `barx` = `(sum x) /(n)`
                                         `barx` = `(60 + 64 + 68 + 69 + 70)/(5)`
                                         `barx` = `(331) / (5)`
                                         `barx` = 66.2        
  Mean difference is given below
                      x                              (x - `barx` )
                    60                         60 – 66.2 =   -6.2
                    64                         64 – 66.2 =  -2.2
                    68                        68 – 66.2 =   1.8
                    69                        69 – 66.2 =    2.8
                    70                        70 – 66.2 =    3.8
  To find the Standard Deviation: Standard Deviation is given by,
                           s = sqrt`(sum x-barx)/(n-1)`)
                    s = sqrt(`((-6.2)^2 + (-2.2)^2 + (1.8)^2 + (2.8)^2 + (3.8)^2) /(5-1)` )
                    s =` (-17.76)/(4)`                            
                     s = -2.09
Mean divided by standard deviation = 66.2/-2.09
Mean divided by standard deviation = -31.67

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Practice problem of mean divided by standard deviation:

Calculate the mean divided standard Deviation for the given data set. 23, 25, 24, 26.
[Answer: 20.41]