Communication
Mean of a group of numbers is simply the average value of those numbers. Thus, mean is the sum of the values in a list divided by the total values in the list. Let us take a sample list of numbers i.e. 1, 6, 7, 7, 9. In this case, the mean is (1+6+7+7+9) / 5 = 6.
Secondly, Mode is that number in a given list which appears the most in the list. In other words the number which is repeated the most times in a list is mode of that list. If one or more numbers are repeated the same number of times, all such numbers shall be mode of that list. In the list mentioned in the aforementioned paragraph 7 is the only number repeated twice, thus the mode is 7. However, in the list 2, 4, 4, 7, 11, 9, 11, both 7 and 11 are modes of the list. It is pertinent to mention that if there is no repetition of a number in the entire list then such a list has no mode.
Third, median is that number in the list which is in the middle of the list when the list is arranged in the increasing order of the numerical values. For instance, if we have list given as 1, 6, 4, 7, 5 then first we will arrange it in the proper order which is 1, 4, 5, 6, 7. Now, the middle number in the list is 5, hence 5 is the median of this list. On the contrary, if the list contains even number of values such as 3, 8, 10, 12 then the median is simply the average of the middle two numbers which in this case will be (8+10) / 2 = 9. However, it is very important that the list is in proper order before calculating the median.
Central Tendency
Mean, Median and Mode, in effect, describe the central tendency of a given data. Central Tendency basically describes the central position of a frequency distribution for a group of data (Descriptive and Inferential Statistics). Those distributions for which mode, mean and median are equal or close to each other have a larger central tendency compare to others. On the contrary, those group of data for which mean, median and mode are largely spaced from each other central tendency is much less and the curve of such data is widely spread. This means that the data for which that particular curve is made is not showing uniform characteristics but varied characteristics. Following are the characteristics of a normal distribution
A list of values is said to be normally distributed when (Lane)
Its mean, mode and median are equal
The area under the curve of the given distribution is 1
When viewed graphically the normal distributions are symmetric around their mean.
Normal Distributions are more dense at the centre and less dense at the tail
The following picture shows a typical normal distribution
Mean, Median, Mode and Range of 1, 4, 4, 6, 7
Mean = (1 + 2 + 4 + 4 + 6 + 7) / 5 = 24/6 = 4
Mode = Most repeated value in the list = 4
Median = Value in the middle of the list when arranged in order = (4 + 4) / 2 = 8 / 2 = 4
Range = Maximum Value – Minimum Value = 7 – 1 = 6
Major Difference between Descriptive Analysis and inferential Statistics
A descriptive analysis basically allows us to study the behavior of a specific group of data. It cannot allow us to make generalizations and present hypothesis beyond the data being observed. This method basically helps presenting the data in a more meaningful way. On the other hand inferential statistics is a tool to make generalizations after the observing the data hence the name inferential statistics. It allows us to make inferences based on the statistics coming out of samples taken from different groups depending on the type of study. However, it is very necessary in this case that the collected samples correctly represent the object of study.
Works Cited
"Descriptive and Inferential Statistics." www.statistics.laerd.com. 13 Jun. 2016. <https://statistics.laerd.com/statistical-guides/descriptive-inferential-statistics.php>.
Lane, David M.. "Introduction to Normal Distributions." www.onlinestatbook.com. 13 Jun. 2016. <http://onlinestatbook.com/2/normal_distribution/intro.html>.
