কোয়ার্টাইল, মধ্যক, সর্বনিম্ন উপাত্ত ও সর্বোচ্চ উপাত্ত নির্ণয়

Five Number Summary

The five number summary is an example of a descriptive statistic. They are values that provide us with the most important features of our data.

Before you attempt to create a five number summary, PUT YOUR DATA VALUES IN ORDER.

Here is the ordered data set:

You've just identified $2$ numbers in your five number summary - minimum and maximum.

Now, let's do the median. If you need a refresher on how to find the median (middle value), click here.

Nice! Now, the only $2$ numbers in our five number summary we need to identify are the first quartile and the third quartile.

Exclude the median value! In other words, the First Quartile is the median of the data less than the overall median, and the Third Quartile is the median of the data greater than the overall median.

Let's look at our data of the kids' ages again:

The first quartile (Q1) is the median of the lower half of our data. This is the data less than the median, not including the median. What is the first quartile? The first quartile is $8$.

The third quartile (Q3) is the median of the upper half of our data. This is the data greater than the median, not including the median. What is the third quartile? The third quartile is $12$.

So, our five number summary:

• Minimum: $7$
• Q1: $8$
• Median: $10$
• Q3: $12$
• Maximum: $14$

We can look at the minimum and maximum values to find the dispersion of the dataset.

Let's try finding the five number summary for a new dataset:

Five number summary on a box-and-whisker plot

Plots can be drawn like so:

Further data analysis can also be done with these plots. We can calculate interquartile range, which is the middle $50$ of the dataset, the difference between the third quartile and first quartile.

We can take this concept a step further by finding the percentile rank.

Another type of data visualization we'll see soon are stem and leaf plots!

(Video) Box and Whisker Plots

by Mashup Math

This video by Mashup Math goes over how to create and understand box & whisker plots.

Summary

We have seen many ways of visualizing data, such as bar graphs, histograms, tables, frequency distributions, and scatterplots. We're going to look at another method of data visualization and statistics.

Say we're given performance data for Jordan's basketball playing.

The first thing we want to do is arrange this data in order from least to greatest. $$5, 10, 16, 17, 18, 20, 32$$ We can see that our upper extreme is $32$. Our lower extreme is $5$. The median is $17$.

When then want to find the median of the upper region and the median of the lower region. The **upper quartile is $20$, and the lower quartile is $10$.

Now we have all of the information we need to construct our plot!

First, we make a number line with all of our data. Then, we mark the five pieces of information we just found.

Then, we make the actual boxes! We make a box that runs through the upper and lower quartiles, with the median in the center. Draw a line through the median.

Then, draw lines on either end, meeting the upper and lower extremes.

What does this type of plot tell us?

• The distribution of a bunch of data points.
• How two data distributions compare to each other.

He then goes over another real-life example!

Box and Whisker Plots

Data visualization is important when we are assessing large amounts of data. One type of data visualization is the box and whisker plot.

Key terms to know:

• Lower extreme: the lowest value of a dataset

• Lower quartile: the median between the median and the lower extreme

• Median: the middle value of the entire dataset

• Upper quartile: the median between the median and the upper extreme

• Upper extreme: the highest value of a dataset