Understanding the Significance of the Mean and Median
Calculating the Mean
The “mean" is calculated by adding all the values of the variables --- recall that in our example, the number of bar soaps produced in each of the 105 job order events represent the variables.
In summing them up, we arrived at a total of 23,420 bar soaps produced. To get the mean, 23,420 is divided by 105, which is the number of job orders, thereby arriving at a “mean" of 223, representing the average number of bar soaps produced.
View the completed graph on your right and take note of the variables that reached peak somewhere between 216-230.
Determining the Median
The median is calculated by dividing the total number of data points into two, which in this case study is the number of job orders. Hence, the median is calculated by dividing 105 / 2 = 52.5 rounded-off to 53.
The sum of the first five set of data points = 3 + 7 + 11 + 12 + 26 = 59
- The sum of the second half of the set of data points = 22 + 12 + 8 + 3 + 7 = 46
Since the median is only 53, we adjusted the trend lines on the fifth bar by plotting up to a height of only 20 in terms of frequencies. The adjustment was derived by extracting the difference between the sum of 59 and the median of 53; to get six (6). The latter was used to determine the new value of the fifth bar by deducting 6 from 26.
Hence, the sum of the first five bars is now calculated as: 3 + 7 + 11 + 12 + 20 = 53
What this sample histogram means is that the peak extends only to 20, and not to the full height of the fifth bar at 26. It is at this point that the production level and the job orders are balanced and where the histogram achieves the normal or bell-shaped distribution.
In interpreting the analysis by way of distribution shape, we can infer that the normal distribution of production is at around 223 bars of soaps for 20 job orders.
Please proceed to the third page for this article's explanations on how to determine the mode and how to figure out a skewed distribution.