TopAt times, in a normal distribution of a statistical data, we would find the need of calculating the upper and lower limits. For instance, finding the upper and lower limits for medicines that should be given to the patients is required to be evaluated. So, let us learn how to find upper limit and lower limit for any distribution as follows:

In graph, the upper limit is shown as U and lower limit as L. We convert half of the % to decimal. In our example, we would get 0.25. Next, we check the Z - table for value we got as decimal number in the previous step. We write the closest value for the answer. In our example, we would get the closest value as 0.2770 for 0.2500.

This score is positive i.e. right hand score on the z - table and is represented as U in the graph.

Next, we substitute this score in the equation:

U = z SD + M

where, SD is the Standard Deviation and M is the Mean of the distribution. Thus, we get the corresponding value of the upper limit. We then find the lower limit L by making the sign of z score as negative and using the same formula again.

L = z SD + M. First, we find out the various quantities we would need, like mean, standard deviation, variance, mid % amount of the distribution. Next, we draw the plot for distribution, such that mean is placed in the middle. We shade the portion on the either side of mean representing the middle %. For instance, if the mean is 50 lt., and we have been asked to find the upper and lower measures for the middle % as 50 %, we would draw the graph as follows: