Median is more than Mean - Interpretation

descriptivestats

#1

Hello Friends,
I recently started learning Data Science modules, of which started with Statistics basics. I came across a situation where i tried to draw Summary Statistics for all the employees time sheet entry in in hours. I just took 1 week data and below is the summary statistics

Average 27.56
Std.Dev 16.69
Median 30.00
Min 0.00
Max 76.77
Mean - std.dev 10.87
Mean + std.dev 44.25

Skewness -0.05
Kurtosis -1.32

I could understand that this is a -vely skewed. But can any one explain me how exactly the employees have clocked the efforts for 1 week. There are 429 employees.

thanks !


#2

@AdarshaG The following are my conclusions from the given statistics:

  1. Mean, the simplest : This means “On an average an employee works around 27 hours a week”

  2. The distribution is skewed to the left : We look at the mean(average) and median, we can clearly see that the mean is less than the median.

We can also look at skewness for this conclusion. The skewness is negative.
What this mean : Majority of your values are to the right of mean or they are greater than the mean . You can say “majority of the employees work more than 27 hours a week”

3.The skewness is quite less:


Our case is the third case : -0.5<skewness<0.5 so we can say the distribution is approximately symmetric or normal

4.If we say the distribution is approximately normal, things get interesting. Look at the following diagram which shows spread of data with respect to standard deviation in a normal distribution:

Some points to note:

  • 68% data lies within 1 standard deviation of the mean.

Notice in our case, I standard deviation is from 10.87 to 44.2. We can say that “approximately 68% of your employees put in work hours somewhere between 10.87 and 44.2 a week.”

5.Min and Max : The max value suggests the highest number of hours by any employee is around 77 in the week (Some people are putting in real effort or should you verify it?) . The min value suggests some employees haven’t put any hour whole week (Were they on sick leave? Is the strange value because of a technical glitch? Maybe the system didn’t take that employee’s reading properly?)

Hope this helps.

Sanad


#3

Thanks to all for your wonderful reply !!!