Question

. Determine which of the following is the best method (histogram, bar chart, box plot, stem and leaf diagram, or pie chart) of displaying the results of the following studies (some may have multiple answers)

a) You concluded a study determining the favorite meal choice (from a list of 5 options) from a sample of 100 people. You want the data displayed so that an individual could easily determine the most frequently favored of these options.

b) You concluded a study gathering information on the weights (in pounds) of 100 individuals. You want the data displayed where an individual could easily determine the most frequent occurring height range (such as 60” to 65”).

c) You concluded a study where you have determined the age where 100 individuals received their undergraduate diploma. You wish to present your findings in a way that someone can easily see which decade (twenties, thirties, forties, etc.) was the most frequent while still being able to view the full set of data.

Answer 1

Before I answer the questions let me take you through a brief understanding of these charts and plots.

1: Bar Chart: A bar chart is made up of columns plotted on a graph. These columns are positioned over a label that represent a categorical/qualitative variable. The height of the column indicates the size of the group defined by the column label.

2: Histogram: A histogram is also made up of columns plotted in a graph. Usually, there is no space between the adjacent columns. Unlike bar chart, here the columns are positioned over a label that represents a continuous, quantitative variable.

3: Stem and leaf plot: The stem and leaf plot shows all the data points in a tabular form. One can study shape of distribution from stem and leaf plot.

4: Box plot: A box plot, also known as a box and whisker plot, is a type of graph that displays a summary of a large amount of data in five numbers. These numbers include median,upper quartile,lower quartile,minimum and maximum value. It is easier to locate outliers in a box plot.

5: Pie-Chart: A pie-chart helps show proportions and percentages between categories, by dividing a circle into proportional segments.

Note: The main difference between bar chart is used to represent categorical variable whereas histogram is used to represent quantitative variables.

Solution:

1: Let the top 5 favorite meal choices be A,B,C,D and E. As we have categorical variable(meal choices), we can either use a bar graph or a pie chart to represent our data.

In bar graph the column having the highest height is the most frequently favored option and in a pie-chart a person can see which meal choice has the most covered area in that circle and hence same will be the most frequently favored option.

2: As weights are quantitative in nature. We can divide our entire data into classes of equal heights.

Suppose minimum weight is 30 kg and maximum weight is 95 kg. We can have classes as 30-35,35-40,40-45,......,90-95

and the corresponding frequencies.

Now, we can represent our data with the help of a histogram and the class which has the highest height is the most frequently occurring height.

You concluded a study where you have determined the age where 100 individuals received their undergraduate diploma. You wish to present your findings in a way that someone can easily see which decade (twenties, thirties, forties, etc.) was the most frequent while still being able to view the full set of data.

3: Age is again quantitative in nature. As we wish to see full set of data and along with which we wish to see which was the most frequent decade in which people received their undergraduate diploma.

The best way to represent this is by using stem and leaf plot, as this enables us to look into entire data as well as gives us a clear picture of which class is most frequently occurring.

Hopefully, this answers all your questions. Regards.