CH.2 frequency distributions and graphs

Constructing a frequency distribution from a data set

1. Decide on the number of classes to include in the frequency distribution. The number of classes should be between 5 and 20; otherwise, it may be difficult to detect any patterns. 2. Find the class width as follows. Determine the range of the data, divide the range by the number of classes, and round up to the next convenient number. 3. Find the class limits. You can use the minimum data entry as the lower limit of the first class. To find the remaining lower limits, add the class width to the lower limit of the preceding class. Then find the remaining lower limits, add the class limit of the first class. Remember that classes cannot overlap. Find the remaining upper class limits. 4. Make a tally mark for each data entry in the row of the appropriate class. 5. Count the tally marks to find the total frequency f for each class.

Constructing an Ogive ( cumulative frequency graph)

1. construct a frequency distribution that includes cumulative frequencies as one of the columns. 2. Specify the horizontal and vertical scales. The horizontal scale consists of upper class boundaries, and the vertical scale measures cumulative frequencies. 3. Plot point that represent the upper class boundaries and their corresponding cumulative frequencies. 4. Connect the points in order from left to right. 5. The graph should start at the lower boundary of the first class ( cumulative frequency is zero) and should end at the upper boundary of the last class (cumulative frequency is equal to the sample size).

cumulative frequency graph, or ogive

A cumulative frequency graph, or ogive (pronounced o'jive), is a line graph that displays the cumulative frequency of each class at its upper class boundary. The upper boundaries are marked on the horizontal axis, and the cumulative frequencies are marked on the vertical axis.

frequency histogram

A histogram is a bar graph that represents the frequency distribution of a data set. A histogram has the following properties. 1. The horizontal scale is quantitative and measures the data values. 2. The vertical scale measures the frequencies of the classes. 3. consecutive bars must touch.

relative frequency histogram

A relative frequency histogram has the same shape and the same horizontal scale as the corresponding frequency histogram. The difference is that the vertical scale measures the relative frequencies.

frequency polygon

Another way to graph a frequency distribution is to use a frequency polygon. A frequency polygon is a line graph that emphasizes the continuous change in frequencies.

class boundaries

Because consecutive bars of a histogram must touch, bars must begin and end at class boundaries instead of class limits. Class boundaries are the numbers that separate classes without forming gaps between them.

lower limit, upper limit

Each class has a lower class limit, which is the least number that can belong to the class, and an upper class limit, which is the greatest number that can belong to the class.

stem-and-leaf plot

In a stem-and-leaf plot, each number is separated into a stem (for instance, the entry's leftmost digits) and a leaf (for instance, the rightmost digit).

cumulative frequency

The cumulative frequency of a class is the sum of the frequency for that class and all previous classes. The cumulative frequency of the last class is equal to the sample size n.

range

The difference between the maximum and minimum data entries is called the range.

class midpoint

The midpoint of a class is the sum of the lower and upper limits of the class divided by two. The midpoint is sometimes called the class mark. Midpoint = (lower class limit) + (upper class limit)/2

relative frequency

The relative frequency of a class is the portion or percentage of the data that falls in that class. To find the relative frequency of a class, divide the frequency f by the sample size n. Relative Frequency = Class frequency/ Sample size=f/n

Pareto chart

a bar graph whose bars are drawn in decreasing order of frequency or relative frequency typically for qualitative data

pie chart

a convenient way to present qualitative data graphically as percents of a whole. It is a circle that is divided into sectors that represent categories

grouped frequency distribution

a distribution used when the data is quantitative, the range is large and classes of several units in width are needed

Categorical frequency distribution

a frequency distribution used when the data are categorical (qualitative)

2.1 A frequency distribution:

is a table that shows Classes or Intervals of data entries with a count of the number of entries in each class. The Frequency f of a class is the number of data entries in the class.

class width

the class width is the distance between lower (or upper) limits of consecutive classes.

ungrouped frequency distribution

when the range of the data values is relatively small, a frequency distribution can be constructed using single data values for each class