2.2-2.3

Summarizing quantitative data:

Determine whether the data is discrete or continuous

  • If the data is discrete & there’s a few different values of the variable, the categories of data (classes) will be the observations (as in qualitative data)

  • If the data is discrete but there are many different values of the variables, or the data is continuous, the categories of data (the classes) must be created using intervals of numbers.


Classes- Categories into which data are grouped

When a data set has a large number of different discrete data values or when a data set consists of continuous data, we have to make classes by using intervals of numbers

Lower class limit- The smallest value within the class

Upper class limit- The largest value within the class

Class width- The difference between consecutive lower class limits

Example:

The lower class limit of first class is 25

The lower class limit of second class is 35

The upper class limit of first class is 34

Class width: 35−25=1035-25=10


Histogram: It’s made by drawing rectangles for each class of data.

  • The height of each rectangle is the frequency or relative frequency of the class

Stem and leaf plot: It uses digits to the rightmost digit to form the stem

  • Each rightmost digit forms a leaf

Example: A data value of 147 would have 14 as the stem and 7 as the leaf

Dot plot: It places each observation horizontally in increasing order and placing a dot above the observation each time it is observed

  • Uniform distribution- The frequency of each value is evenly spread out across the values of the variable

  • Bell-shaped- The highest frequency is in the middle and the frequencies tail off to the left and right

  • Skewed right- More data at the left

  • Skewed left- More data at the right

Determining the Lower Class Limit of the First Class and Class Width:

Choosing the lower class limit of the first class

  • Choose the smallest observation in the data set or a convenient number slightly lower than the smallest observation in the data set


Determining class width

Pick on the number of classes

  • The smaller the data set, the fewer classes you should have

Class width: largest data value - smallest data value / number of classes

  • Round this value up to a convenient number


Guidelines for good graphics:

Provide explanations if needed and include units of measurement

Never lie about data

Minimize the amount of white space in the graph

if the scale is truncated, indicate this to the reader

Avoid clutter and unnecessary backgrounds or pictures

avoid 3D graphics