CORPFIN 7033 Quantitative Methods

Question:

This homework will focus on histograms or averages.

1) Check out the Video on Histograms.

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2) Download the Histograms Booklet. Do exercises 1 to 4 starting on page 18.

If you are asked to choose a state for the first question, any state is acceptable.

3) Check out the video on Measurement of center

3) Download the measures-of-center student guide.

Do the Review questions 1 through 3 on pages 17-18.

Answer:

Figure 1 shows a histogram chart that would be displayed if a class interval was 500,000.

Christiansen defines class interval as the area in which the range of a variable can be separated. This is represented by the divisions of a bar chart or a Histogram (11).

In this instance, the Illinois State is chosen.

The State of Illinois’s population of residents 65 years and older is 1,609,000. It falls within the 1,500,000-2,000,000 range.

Given that the media of distribution is 1,000, 000, it can be assumed that the Illinois resident 65-year-olds are closer to what would be considered typical.

The figure shown above has one peak, and the result is slightly skewed.

Wegman identifies a single peak as a “unimodal” distribution (138).

Because this distribution isn’t a normal distribution, it would have a different mean, mode, and median.

Figure 2 contains both gaps and outliers.

Christiansen refers to a gap when a point is found in a given distribution but has no data. (12) A gap is a value which is significantly less or greater than any other data in a set.

Figure 2 contains gaps between classes at intervals of 2,500,000-3,000,000 and 3,500,000-4,000,000. There are also outliers between classes 4,500,000-4,000,000 and 5,500,000-4,000,000.

These two classes have a much lower y-axis values than the rest.

An increase in class width will reduce the number of classes.

Outliers and gaps are also eliminated in this model.

But, the distribution’s shape is the same.

Illinois has a 12% percentage of residents aged 65 and over. This is very close to the national average, i.e.

This means that Illinois has a population of 65 and over.

This case, the histogram’s columns form a symmetrical shape called a bell shape.

The distribution’s median, mean and mode are therefore equal.

Wegm says that a normal distribution is one with a peak at the top of the middle (146).

The columns of this histogram resemble the columns in Figure 1, which shows Americans 65 years old and older.

This means that the sample (residents aged 65 and over) is representative for the distribution of total populations.

Asymmetrically, the distribution curve is also distorted to the right. The unimodal peak, which means that the mean, median, and mode of the distribution are not equal, creates a unimodal peak.

States with unusually large populations fall within the classes with 3,500,000-4,000,000 and 3,500,000-3,500,000 respectively. These classes have a much lower y-axis than the other classes.

This observation is identical in nature to those made under Figure 1. It shows residents 65 years old and older.

Data breaking strengths vary according to observation.

Wegm states that you can observe the data breaking strengths by looking at maximum and minimum values in a particular model (149).

The maximum breaking strength of this model is 168, which is the highest value. The minimum breaking strength is only 115 which is the lowest.

The most data was in the class interval 160 –165. There are 6 observations. The histogram columns for this class are the longest.

This histogram has a skewed breaking strength to the left. The median is the “middle” number in the set.

Works citées

Christiansen S. “Visual presentation of data.”

AMA Manual of Style, vol.

“John Wiley & Sons” will launch Data Mining and Statistical Analysis in the early part of 2007.

Statistical Analysis and Data Mining 2007 doi:10.1002/sam.100.

“Special issue in statistical analysis, data mining.”

Statistical Analysis and Data Mining. Vol.

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