BUSINESS STATISTICS

October 29, 2015

Average Temperatures

T Newark J Martinez

{Modules 1, 2, & 3 Contributions combined}

A. Purpose of Project The purpose of our data collection was to find the average temperature for the United States on a given day in the month of October. It can be speculated that a sampling of any 30 cities in the U.S. would produce an accurate average temperature result. Many businesses could find this data useful when making business decisions. B. Collect Data The data was surveyed from "The Gazette ", which is the local Colorado Spring newspaper. This publication provides a national temperature chart by the National Weather Service. The sample data was taken from the October 5, 2015, online edition. We selected this source for the data, due to the fact this publications is reputable and obtains it's information from a national source. The temperature from every third city, beginning with the second city in the list, was used. C. List of Raw Data Raw data from the sample of 30 data points are presented below in order from lowest to highest temperatures, in oF :

48, 57, 58, 64, 64, 66, 68, 69, 69, 70, 72, 73, 73, 73, 73, 76, 83, 83, 83, 84, 84, 86, 86, 86, 87, 87, 87, 87, 88, 89.

D. Frequency Distribution

Temperature (F)

Class Frequency

Relative Frequency

(%) Cumulative Frequency

Class Midpoint

40 < 45 0 0 0 43 45 < 50 1 3.3 1 48 50 < 55 0 0.0 1 53 55 < 60 2 6.7 3 58 60 < 65 2 6.7 5 63 65 < 70 4 13.3 9 68 70 < 75 6 20.0 15 73 75 < 80 1 3.3 16 78 80 < 85 5 16.7 21 83 85 < 90 9 30.0 30 87

30 100.0

E. Histogram

The data appears to be negatively skewed with more clusters of cities with higher temperature.

F. Relative Percentage Polygon

The relative percentage polygon indicates negatively skewed data. G. Sample Mean

The sample mean is 75.77 oF.

H. Sample Median

The median temperature is 74.5 oF. I. Sample Mode

This data set has two modes; both 73 oF and 87 oF were reported by four different cities.

J. Sample Range The highest temperature reported was 89 oF and the lowest temperature reported was 48 oF. Therefore, 41 oF separates the highest from the lowest temperature.

K. Sample Variance The data shows the sample variance to be 119.9 oF2.

L. Sample Standard Deviation The sample standard deviation is 10.95 oF.

M. Coefficient of Variation The coefficient of variation of 14.45% by itself has no meaning, however this coefficient of variation could be used to compare this set of data to other data sets.

N. Z-scores city temp

0F Z-scores 48 -2.5160 57 -1.6941 58 -1.6027 64 -1.0548 66 -0.8721 68 -0.6895 69 -0.5982 70 -0.5068 72 -0.3242 73 -0.2329 76 0.0411 83 0.6804 84 0.7717 86 0.9543 87 1.0457 88 1.1370 89 1.2283

Since none of the city temperatures had a Z-score of greater than +3 or less than -3, none of the temperatures would be considered outliers.

O. Initial Analysis of Data The histogram and percentage polygon showed a negative skew. On the other hand, the mean temperature was greater than the median temperature, so the data would be considered positively skewed. This data appears to be a bi-modal distribution due to these two contradictory observations. The likely reason for this is having data from U.S. cities in the northern and the southern parts of the country during the autumn month of October. In any case, the data is definitely not normally distributed.

I. Module 3 Contribution

A. Type of Sampling and Recommendations for Improvement

The sampling frame used was the list of U. S. cities and their high temperatures seen in the October 5, 2015, online edition of the Colorado Springs Gazette. Since the data was already organized in an alphabetical list, systematic random sampling was used, recording the temperature from every third city beginning with the second city in the list. This was simple and easy to do, however, since the data was already organized, there was a possibility of severe selection bias.

B. Confidence Interval

Our 95% confidence interval was found to be 75.77 oF ± 4.09 oF = 71.68 oF to 79.86 oF, using the sample standard deviation, 10.95 oF and the sample size of 30 in the Excel function CONFIDENCE.T.

C. Revised Sample Size

We were asked to use a minimum of thirty data points for this project. Now having calculated the sample standard deviation and considering a desired range of temperature data to be ± 2 degrees, we can calculate a revised sample size: n = ((1.96 x 10.95) / 2)2 = 115.15. This revised sample size of at least 116 cities would be used for the next round of sampling.