Question

Exercises For Conceptual Understanding 1. Define and distinguish between a frequency distribution, a relative frequency distribution, a cumulative frequency distribution, and a cu ori 3. When should one use a bar graph instead of a mulative relative fre quency distribution. 2. Why do the ends of a polygon touch the h zontal or X-axis? histogram and a pie chart instead of a relative frequency polygon? Inwan the hars

Answer 1

1.

Frequency distribution:

The frequency distribution of events is the number of times each event occurred in an experiment or study.

Frequency distributions can be displayed in a table, histogram, line graph, dot plot, or a pie chart etc.

Relative Frequency Distributions:
A relative frequency is the fraction or proportion of times a value occurs. To find the relative frequencies, divide each frequency by the total number of data points in the sample. Relative frequencies can be written as fractions, percents, or decimals. Relative frequencies can be written as fractions, percents, or decimals. The column should add up to 1 (or 100%).
The only difference between a relative frequency distribution graph and a frequency distribution graph is that the vertical axis uses proportional or relative frequency rather than simple frequency.

Cumulative Frequency Distributions:
A cumulative frequency distribution displays a running total of all the preceding frequencies in a frequency distribution.
To create a cumulative frequency distribution, start by creating a regular frequency distribution with one extra column added.
To complete the cumulative frequency column, add all the frequencies at that class and all preceding classes.
Cumulative frequency distributions are often displayed in histograms and in frequency polygons.

Cumulative Relative Frequency Distributions:
Just like we use cumulative frequency distributions when discussing simple frequency distributions, we often use cumulative frequency distributions when dealing with relative frequency as well. Cumulative relative frequency (also called an ogive) is the accumulation of the previous relative frequencies. To find the cumulative relative frequencies, add all the previous relative frequencies to the relative frequency for the current row.

2.

To create a frequency polygon, start just as for histograms, by choosing a class interval. Then draw an X-axis representing the values of the scores in your data. Mark the middle of each class interval with a tick mark, and label it with the middle value represented by the class. Draw the Y-axis to indicate the frequency of each class. Place a point in the middle of each class interval at the height corresponding to its frequency. Finally, connect the points. You should include one class interval below the lowest value in your data and one above the highest value. The graph will then touch the X-axis on both sides.

3.

Bar charts and histograms can both be used to compare the sizes of different groups. A Bar chart is made up of bars plotted on a graph.

Histogram is a chart representing a frequency distribution; heights of the bars represent observed frequencies. In other words a histogram is a graphical display of data using bars of different heights. Usually, there is no space between adjacent Bars.

Bar Chart

The columns are positioned over a label that represents a categorical variable.
The height of the column indicates the size of the group defined by the categories.

Histogram

The columns are positioned over a label that represents a quantitative variable.
The column label can be a single value or a range of values.
Here is the main difference between them. With bar charts, each column represents a group defined by a categorical variable; and with histograms, each column represents a group defined by a quantitative variable.