The Mode, The Median, and The Mean – All About The 3 Main Measures of Central Tendency
Some people might find the mention of statistics utterly boring, but Six Sigma practitioners that have completed their Lean Six Sigma Green Belt training are aware that Six Sigma projects would not be successful without them. Simply said, statistics is an essential component of data-driven projects that use the Six Sigma methodology. When you reach the Green Belt level of Six Sigma, it’s necessary to comprehend several statistical techniques on a fundamental level. Green Belts and Black Belts in Six Sigma frequently make calculations using statistical programs like MINITAB. Nevertheless, it is really beneficial to comprehend the guiding ideas behind a measure, including the central tendency measures.
According to trustworthy free online Lean Six Sigma training courses, statistical techniques are employed during the “Measure” & “Analyze” steps of the DMAIC (Define, measure, analyze, improve, and control) process. Measures of central tendency are the most fundamental statistics any Six Sigma practitioner is going to examine. At the top of the list of things Six Sigma teams need to look at following data collection are the measures of central tendency.
Statistics And Its 2 Branches
First, let’s examine two statistical subfields. Descriptive statistics is referred to as branch no. 1, while inferential statistics is branch no. 2. These are the main two branches of statistics. A process, population, or sample’s characteristics like location (measurements of central tendency), shape (skewness & peaks), and/or spread (variation) are all described using descriptive statistics. As a result, central tendency measurements are a subset of descriptive statistics.
Based on samples of information collected from some population, inferential statistics draw conclusions and forecasts about that population using the data. These are often applied in the DMAIC process’ “Analyze” phase.
What Exactly Are Measures of Central Tendency?
The central placement inside a sample of information is identified by using measures of central tendency, which are single values that aim to explain any set of data. Measurements of central location are another name occasionally used to refer to measures of central tendency. To put it another way, it is a metric that identifies the location of the center of a data set. The most popular measure of central tendency is called the mean, also known as the average. The median & the mode are two further measures of central tendency. The measures of central tendency that are valid include the mean, the median, and the mode.
Mean: The First Measure of Central Tendency
The most well-liked and recognized of the measures of central tendency is “the mean”, commonly referred to as “the average”. Although it may be utilized with continuous and discrete data, continuous data is more frequently used. The mean is determined by dividing a data set’s total number of values by the same data set’s sum of all values. Consequently, the following would be the mean formula: sum of all items divided by the number of items.
How Do You Figure Out The Mean?
Let’s check out some examples in order to better understand every measure of central tendency. First, we have an example to find the mean.
(1+2+3+4+5+6+7+8)/8 = 36 / 8 = 4.5
The sum of the numbers from one to eight was divided by the total number of items (8). Therefore, 4.5 is the result. The mean or average is 4.5.
62+68+72+60+50+58+58+49+66+70 / 10 = 61.3
For example 2, we have a collection of data that will be analyzed to find the mean. Let’s say you want to calculate the average waiting time at a clinic, so you take down notes of how long every patient had to wait for their turn. To determine the average, the data for ten patients were gathered on a particular day. Minutes were used as the measuring unit for data collecting. We added together the waiting time for ten different individuals, divided the total by the number of items on the equation, and got the mean waiting time for all patients. The answer here is 61.3 minutes. There is a 61.3-minute timeframe here. That is how the most popular measure of central tendency works.
Median: The Second Measure of Central Tendency
The median, also referred to as the positional average, is another measure of central tendency. Positional averages are determined by where an observation is located within a sequence of observations that are ordered in either descending or ascending order. The value that divides a group into 2 equal portions, one consisting of all values larger than the median, and the second one of all values smaller than the median, is known as the median. Basically, when a set of numbers is sorted in a specific way, either largest to smallest or the other way around, the number that falls in the center of the sequence will be called that set’s median.
How Do You Figure Out The Median?
The median’s formula is written as n + 1 / 2. The value located at the spot provided by this formula’s answer will be called the median. Let’s consider the following examples.
62+68+72+60+50+58+58+49+66+70 / 10 = 61.3
The formula has been used to keep count between the first and last number. It brings the answer to 4.5, but 4.5 is not the median. The median value is the one that stands in the 4.5th place. So, how would we determine the value that occupies the 4.5th spot, then? The calculation we need to do would be taking the fourth value, adding half of the fifth value, and then subtracting the fourth value.
We’ll be using the same waiting time situation we used before for example no. 2. The waiting time information was arranged in increasing order. We must count the amount of data and create the formula to get the median. The answer in this case is 5.5. The median value is the one that stands in 5.5th place. Consequently, 61 minutes will be the median.
Mode: The Third Measure of Central Tendency
The figure in a population that appears most frequently is referred to as the mode. The most items are found in and surrounding it, and it’s a real value. Let’s see the following examples to understand it better.
1+2+3+4+5+5+6+7+8 = 5
In example 1, 5 is the value that appears most frequently. That means the mode for this collection of data is 5. In example 2, the collection of data had three instances of the 10 and 7 values, so, the mode is going to be between 10 and 7.
- 12,10,15,24,30 (No Mode)
- 7,10,15,12,7,14,24,10,7,20,10 (The Mode is 7 & 10)
A formula is always needed, otherwise nothing in statistics would function. You must have the formula you want to use for every statistical operation you want to solve. Naturally, all of the central tendency measures can be quite simple to compute using software programs like Microsoft Excel, but it is still beneficial to know the right way to do it manually.
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