Part+2-+Analysis+of+Data

__Analysis__
Analysing data is what we do after we have finished collecting it. While analysing the data, we usually measure the frequency of response, abnormalities and average of data collected. When analysing data in statistics, the three most important terms are the **mean**, **mode** and **median**. This way, we are actually breaking the results up into categories to understand them better. We may also see trends when analysing results, thus leading to interpretation and conclusion.

Below, we explain about the three important terms used in analysis of statistics:

__Mean__
The mean of the overall data also refers to the average of the Data. Here is an example: Total Number of Groups: 10 Total Number of Toys: 3+4+5+6+8+12+7+3+8+9=65 Mean(Total Number of Toys/ Total Number of Groups): 65 ÷ 10 = 6.5
 * Name of Groups || A || B || C || D || E || F || G || H || I || J ||
 * Number of Toys || 3 || 4 || 5 || 6 || 8 || 12 || 7 || 3 || 8 || 9 ||

In this case, the mean is 6.5. It is also an accurate mean (average) of the total number of toys.

However, the mean can also be distorted. Here is an example:


 * Name of Groups || A || B || C || D || E ||
 * Number of Toys || 2 || 2 || 3 || 41 || 76 ||

Total Number of Groups: 5 Total Number of Toys: 2+2+3+41+76=124 Mean:

124 ÷ 5 = 24.8

In this case, the mean is 24.8. However, The mean is distorted as there are extreme values (Number Difference too big from majority of numbers), which are 41 and 76. The number distribution is not normal as there are both low and extreme numbers. Thus, when the mean becomes distorted, the result becomes inaccurate.

__Median__
The median of the data is middle value of the data (must be arranged in ascending or descending order). It is usually used when there is an uneven distribution of numbers in statistics. We have split the ways of finding the median into two different groups, **Odd** and **Even**.

Here is an **Odd** example: 1 4 5 6 8 11 15 17 21 23 25 31 47 56 58 63 65 69 77

There are 19 numbers in total. Therefore, the median is the 10th number (middle value), which is __23__.

Here is an **Even** example: 1 2 2 3 3 4 7 18 24 34 54 55 57 62 63 68 69 74 78 81

There are 20 numbers in total. However, since 20 is an even number, the middle values are both the 10th and 11th numbers, namely 34 and 54 respectively. So, in this case, we take the average of both numbers, which is:

(34 + 54) ÷ 2 = 44

Therefore, the median is is the average of 34 and 54, which is __44__.

However, the median can be distorted. Here is an example: 1 2 2 65

There are only 4 numbers in total. So, we take:

(2 + 2) ÷ 2 = 2

In this case, the median is 2. However, in this case, the median becomes distorted as there are too few number samples ( there are also extreme values). The median's accuracy depends on the number of data samples, and thus, the more number of data samples, the more accurate the median becomes.

__Mode__
The mode of the data is the sample/number that occurs most frequently in collected data. It can be used to find out abnormalities and frequency of samples. Here is an example:
 * Name of Child || Tom || Jerry || Sam || Samuel || Jack || Raju || Rick || Ben || John || Kate ||
 * Number of Sweets Given || 2 || 3 || 3 || 2 || 4 || 3 || 4 || 7 || 6 || 1 ||

In this case, the number 3 has the most occurrences (3 occurrences), and therefore the mode is __3__.
 * Number || 1 || 2 || 3 || 4 || 6 || 7 ||
 * Occurrences || 1 || 2 || 3 || 2 || 1 || 1 ||

However, like the mean and median, the mode can also be distorted. Here is an example:
 * Name of Child || Tom || Jerry || Sam || Samuel || Jack || Raju || Rick || Ben || John || Kate || Jess || Joseph || Rose || Ahmad ||
 * Number of Sweets Given || 2 || 4 || 2 || 4 || 3 || 2 || 3 || 4 || 6 || 1 || 3 || 7 || 10 || 9 ||

The mean is distorted as there are too many equal amounts of samples(2,3 and 4). So, in this case, the mode is impossible to calculate. The mode is basically a crude measurement and is not useful when there are too many equal amounts of samples with the highest frequency.
 * Number || 1 || 2 || 3 || 4 || 6 || 7 || 9 || 10 ||
 * Occurrences || 1 || 3 || 3 || 3 || 1 || 1 || 1 || 1 ||


 * Now that you have the power of analysis, go on to the next step!**