Statistics & Probability - Unit 2 - Describing Quantitative data

Today's post is about displaying and describing quantitative data

There are various ways to describe quantitative data

Some of them are

- frequency tables : Frequency tables display the frequency of the variable over different values of the variable

e.g.

The following frequency table shows the number of hours of sleep that each of the staff members at Tia's Toy Store got on Thanksgiving night.

Number of hours of sleep	Number of employees
$3$3	$1$1
$4$4	$0$0
$5$5	$4$4
$6$6	$2$2
$7$7	$1$1
$8$8	$1$1

- dot plots : Dot plot shows the frequency of a variable by the number of dots at a given value
e.g.

The following dot plot shows the daily high temperature in Kats, Colorado in April. Each dot represents a different day.

$0$$2$$4$$6$$8$$10$$12$$14$$16$$18$$20$$\text{Temperature }(^\circ\text{C})$

- histogram
Histograms sum of the number of values in a range and the graph them as a bar chart

e.g

- stem and leaf plots - Stem and leaf plots uses a table to display data. The stem of the left side displays the first digit or digits. The leaf on the right displays the last digit.
For example, 543 and 548 can be displayed together on a stem and leaf as 54 | 3,8.

- Box and whisker plot

Below is a box and whisker plot. This plot divides the data into 4 quadrants. The center box is for the 2nd and 3rd quadrants of the data. The left and right lines are for 1st and 4th quadrants. The center line is exactly at the median of the distribution and divides the 2nd and 3rd quadrants. 

Next we will talk about shapes of distributions

Looking at the distribution we can determine the following

- whether the distribution is symmetrical (same shape both sides of the center)
- we can also see whether the distribution is skewed to the left or right. It is skewed to the left if most of the data is to the right and vice versa.
- what the spread ( difference between the max and min value) is
- where could the median lie.