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Statistic Reviewer
One Variable Analysis



Boxplot is also called Box and Whisker plot. Why do you need to learn this? Because if you are using enterprise corporation software like Tableau software for data visualization, you will encounter Box and Whisker plot as one of the options. So as a student to become college and career ready, you need to acquire this knowledge. Important to remember

1. Always arrange your data point from lowest to highest
2. Count the number of your data points. The number of count is represented by letter variable "n".
Now you can answer the question what is the value of lower whisker? = 70 answer
3. minimum value is also called the lower whisker

You also answer the question what is the value of maximum whisker? = 78 answer
4. maximum value is also called the maximum whisker

Now if you are ask,"Tell me what is the median or middle value of your ordered data point ?" You see the middle is between 73 and 75. So you are confused, which one? To solve that confusion, statistician created the rule to get a uniform answer. The rule is you add the two middle number and divide it by 2. Now everybody agreed the median value is 74.

Median is also called the second quartile meaning 2/4 simplifying the fraction becomes 1/2 which correspond to the middle or median of your ordered list.

5. First quartile (1/4) , represented by variable name, Q1 means from overall median (1/2) to the minimum , you find the middle (1/2) value. In fraction 1/2 * 1/2 = 1/4. The word quarter means 1/4. From your ordered list of student's grade, the first quartile (Q1) student has a grade of 71.

6. Third quartile (3/4), represented by variable name, Q3 means from overall median (1/2) to the maximum, you find the middle (1/2) value. Why it is called third quartile? because you are counting the equal sharing from the minimum up to the third quartile line. Mathematically you added the first quartile (1/4) + second quartile (1/4) + third quartile (1/4) = 3/4 . So what is the grade of the third quartile (Q3) student? = 76 answer

7. the rectangular box is also called the inter-quartile, the range between Q3-Q1. Mathematically 3/4 - 1/ 4 = 2/4 = 1/2 = 0.50 in decimal = 50% in percentage

Why is the box or inter-quartile important? Because some decision makers want to know the range of the 50% of the population of data being analyze, " Tell me what is the range of grade of 50% of the student population ? ". Just by looking at the box, decision maker can answer that question quickly, the range of student's grade representing 50% of the total population is from 71 to 76. The short cut is just read the first quartile (Q1) value and the third quartile (Q3) value from the box and whisker plot. You should know by now where is the Q1 and Q3 location from the graph.

Very important to remember: Always arrange from lowest to highest all the given data points if you are using manual method.Then you can do the basic statistical analysis. For example what is the median, mean, deviation, percentile, and so on. You see if your data points is in thousands or millions it will take a long time for human expert to do the manual statistical analysis. So the experts created computer program so they don't need to do the hard work of arranging the data points from lowest to highest. But still human experts ask the important question and do the interpretation.

Shown below is a normal quartile plot and Histogram Graph. These two graphs give the user the ability to answer quickly different question such as:

1. Can you tell me how many student received a third quartile (Q3) grade? = 2 answer.

2. Can you tell me how many student received a maximum grade of 78? = 3 answer

3. How many student get a median grade or second quartile? = 0 answer from Histogram.

If the data points are so big in millions. Like for example the number of U.S. students are in millions. It is very hard to use the traditional manual statistical tools and visualization to answer important question and gain insight to do intervention for improvement. But thanks to machine learning we have now the tools to do another way of analysis that deals with big data.


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