Use of Graphs for Investigate Distributions

Investigate Distributions with Graphs

Part 1

1. Explain the difference between a categorical variable and a quantitative variable

The difference between a categorical variable and a quantitative variable is that the latter is one that fluctuates and changes in amount whereas a categorical variable is one that changes in kind. Basically, variables that are categorical have dissimilar values or categories and there is no distinctive ordering to these categories along a primary measurement. The inference of this is that the categories are simply labels that distinguish one group from another. In contrast, variables that are quantitative are those in which individuals are apportioned numerical values to position them into dissimilar categories. Moreover, these numerical values are meaningful in the sense that they imply more or less of a fundamental measurement that is theoretical interest (Jaccard and Jacoby, 2010). For instance, categorical variables would consist of gender and college major. On the other hand, quantitative variables consist of speed of response as well as loudness (White and McBurney, 2012).

2. Explain what is meant by the term distribution of a variable

The distribution of a variable is a delineation of the relative numbers of times every possible outcome will take place in a number of trials.

3. Determine the difference between a pie chart, a bar chart, and a histogram

A bar chart consists of columns that are plotted on a graph. The columns within the chart are placed over a label that signifies a categorical variable. The height of the column is indicative of the size of the group that is being defined by the column label. Notably, bar charts should be utilized when displaying quantities that are either not necessarily associated or show change in the course of time. For instance, a bar chart is used to show the revenues generated by a firm over the past umber of years. Secondly, similar to a bra graph, a histogram consists of columns that are plotted on a graph. However, with respect to its display, a histogram is different from a bar graph in the sense that it does not have any space in between the columns. Moreover, another difference is that the columns are placed over a label that signifies a continuous numerical variable. the height of the column is indicative of the size of the group that is being defined by the column label. Lastly, pie charts can be delineated as circles that are fragmented into different portions on the basis of the percentage of every category. Pie charts signify percentages of a whole and ought to be used when the data displays how dissimilar categories relate to the whole at a certain point in time. For instance, a pie chart can be used to demonstrate expense categories in relation to the total expenses incurred by a company (Hair, 2015).

4. List different properties one can use when describing the shape of distribution

There are different properties that can be used when delineating the shape of distribution. To begin with, distribution of data can be either symmetrical or asymmetrical. On one hand, with respect to symmetrical distribution, the two sides are a reflection of one another. An example of symmetrical distribution is the normal distribution where the columns create a shape that resembles a symmetrical bell shape. On the other hand, with regard to asymmetrical distribution, the two sides do not resemble one another. A distribution can be positively skewed and this means that the right-side tail is longer in comparison to the left side tail. In contrast, it is negatively skewed when the left side tail is longer in comparison to the right-side tail. Other properties of distributions consist of uni-modal, bi-modal and multimodal distributions. To begin with, a distribution that is deemed to be uni-modal only has one peak in the distribution. As for bi-modal, there are two values that take place more frequently as compared to others. For a distribution that is multimodal, there are several different values occurring more frequently (Australian Bureau of Statistics, 2013).

5. Here are the exam scores of 10 students in a statistics class: 50 35 41 97 76 69 94 91 Create a stem plot for this data set. Use the tens digits as the stem

To create the stem plot, every score is split into two pieces, which are the leaf and the stem. In this case, the digits that represent the tens value are the stems whereas the digits that represent the ones value are the leave. As a result, the subsequent stem plot generates a distribution of the data that is akin to a histogram, however all the values of the data are maintained in a compact form.

The score given are:

When rearranged in an orderly manner, the scores are:

Therefore, in this case, the stems are 2, 3, 4, 5, 6, 7, 9

The stem plot can be represented as follows:

6. Describe a time plot and explain when it is appropriate

Time plots are appropriate when examining the key characteristics of a time series and as a result becomes possible to gain more understanding into observations made over time by plotting them. Imperatively, when examining a time plot, it becomes possible to perceive a general pattern in addition to strong deviations from the pattern. Moreover, it is these patterns within a time plot that can make it possible to have a more extensive understanding of the data (Van der Merwe, 1999).

Part 2

1. The number of deaths in 2011 were: accidents, 12,032; suicide, 4688; homicide, 4508; cancer, 1609; heart disease, 948; and congenital defect 429.

a) Use Excel to make a bar graph to display this data.

b) Suppose that the number of deaths due to all other causes is 5,786. Use Excel to create a pie chart for this data set. 

2. The sales manager at a certain company is trying to decide how much of the budget to allocate for sales personnel for the upcoming year. Typically, sales costs run about 15% of Sales. To help develop an estimate, the sales manager studies sales (in millions $) during the past 2 years at company X, which are given in the table below.

Month

Sales

January

February

March

April

May

June

July

August

September

October

November

December

January

February

March

April

May

June

July

August

September

October

November

December

a) Use Excel to create a histogram for sales. Use class widths of 25 and begin with 225. The class endpoints should be 225, 250, 275, …, 450.

b) Create a time plot for this data. The horizontal axis should indicate the month

3. A group of doctors were interested in testing diets intended to lower blood pressure. Before they began their experiment, they randomly selected a group of 50 people and determined their BMI. The results are provided below.

a) Use classes with endpoints 15, 16, 17, … , 34 and count the number of people in each class.

Bin

Frequency

More

b) Use Excel to create a bar chart for this summarized data. Make the gap width zero to obtain a histogram. Copy and paste your Excel chart into your Word document.

The bar graph with the summarized data is illustrated below.

The histogram obtained from the bar chart above is illustrated below:

c) Describe the shape of the histogram.’

The shape of the histogram is skewed to the left

Subject

BMI

Percent Fat

4. The monthly return of a stock is the change in its market price plus any dividends received during the month. The figure below provides a histogram of the monthly returns of a hypothetical stock for Company ABC.

i. Describe the overall shape of this distribution.

The overall shape of this distribution is a uni-modal one. This is for the reason that there is only one peak point in the distribution. The peak point in the distribution is 20, which is the highest compared to other values. Moreover, the distribution has a bell-shape and therefore can be considered to be a normal distribution.

ii. Indicate the approximate center of this distribution

The approximate center of this distribution is 2

iii. Determine the largest, approximate, monthly return range.

The largest, approximate, monthly return range is 20

iv. Indicate the most likely interval of returns.

 The most likely interval of returns is 4

5. Go to the Pew Research website and find an article supported by a visual presentation of data that you find interesting.

i. Write an essay that describes the main points of the article

The article selected from the Pew Research Website is titled ‘Economic Issues Decline Among Public’s Policy Priorities’. The main points highlighted from the article encompasses the deterioration of economic issues amongst the general public’s policy issues. Different from before, the public do not perceive economic issues as being of high priority. In the contemporary, most of the public consider issues dealing with addition, transportation, and the environment to be of great importance. A number of years back, Americans considered economic issues such as enhancing the job circumstances, fortifying the economic structure and decreasing the budget shortfall to be significant policy concerns, an aspect that has drastically changed now. In the present day, the proportion of Americans claiming that safeguarding the environment ought to be a key policy priority has increased from 44 percent to 62 percent. In the same light, the percentage of Americans claiming that enhancing the transportation system in the United States and dealing with drug addiction among the public to be top priorities has increased from 36 percent to 49 percent (Pew Research Center, 2018). The article basically delineates the change in the perspective of the Americans as to what the government administration ought to consider to be important and act on immediately.