Mathematics and Statistics Quiz Sample Discussion.
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Topic:
Any topic (writer’s choice)
Type of paper:
Essay (any type)
Discipline:
Mathematics and Statistics
Format or citation style:
APA
Pages: 4
Deadline: 19 hours
PART 1
identify a variable (a parameter you want to study in a population) for which you will collect, organize, summarize, and analyze a set of data. You will then prepare a report of your study following the steps described below. Since you will be performing calculations on the data, your variable should be measured at the interval or ratio level (no qualitative or ordinal level variables). You should have at least 30 observations in your data set.
1. Provide a detailed description of your study.
o What it is about and what the variable of study is.
2. Describe how the data were collected
o Were the data collected over a single 2-hour period? Over several days? Copied off a webpage? What sampling method was used?
3. Include the total number of observations in your data set.
o Present your unorganized data in a list
4. Organize the raw data into a frequency distribution with 6 classes.
o Make sure your table includes class boundaries, tally marks, frequency, relative frequency, percentage, and total frequency. Place this table on the upper half of a new page
5. Create a histogram of your data
o Label and title your histogram properly. Use midpoints on the horizontal axes. Put on top of each class the actual frequency and within each box the corresponding percent. The histogram goes to the lower half of the page that has the frequency table.
6. Calculate the five-point summary of your data set. Include a whisker and box plot along with the five-point summary on a separate page and place them on the upper half of the page.
7. Calculate the mean, median, mode(s), variance, and standard deviation for your data set. Place the results under the whisker and box plot.
8. Describe the distribution
o Is the shape symmetric, skew? Skewed right or left? Why? Include that description with the reason at the bottom of the page that has results from steps 6 and 7.
9. Which of the measures of central tendency do you think best describes your data? Why?
o Is it the mean or the median or the mode that you’d report if you had to sum it up to a single number?
10. Are the results of your study what you expected? Why or why not. Write one paragraph conclusion.
Part II
Now, think of another variable that might be correlated to the one in Part I. Collect the values for that variable and tabulate the outcomes with headings X and Y in two rows, where Y represents the variable you collected first, and X represents the other one
1. Display the data set as a scatter plot including the best line.
2. Compute the regression line y=mx+b (best-fit) line.
o Explain the meaning of m within the context.
o Explain the meaning of b within the context if it makes sense.
3. Compute the correlation coefficient.
o Interpret the result. Are they positively strongly/weakly related, or negatively strongly/weakly related?
4. Compute the coefficient of determination.
o What percent of the results in the Y variable (Response or dependent variable) can be explained by the X variable (Explanatory or independent variable).
5. Write a brief conclusion summarizing the relation between X and Y. Is the result what you expected? Explain.
Summary:
Write a brief paragraph to present your work to someone who did not read the rest of the report.
Use excel to do the graphing etc.Use Microsoft Word, Times New Roman, double space. Itemize your answers as above and use the given question as the heading and highlight it. For example:
8. Describe the distribution (i.e., its shape, skewness).
Your answer here (not highlighted)
Make sure items 4, 5 are on a page and 6,7,8 on another. Make sure the table and scatter plot of the second part are on the same page. Write your overall summary on a new page. Include a cover page.
Part I
The study involves a review of the life expectancy for the United States population for the years 1985 up to 2013. The data to be analyzed was copied off from the center of disease control and prevention, CDC, website where it was collected by the national center for health statistics, NCHS. The variables in the data were years (from 1900-2015), sex (male and female), race (black and white), average life expectancy in years and the age adjusted death rate. The current study considered the average life expectancy in years and the age adjusted death rate of the recent years 1985 to 2013 inclusive of all races and both sexes. Therefore, out of the given 116 observations, 30 were used for the study.
The data is as follows;
Frequency distribution table
| lower bound | upper bound | tally | frequency | relative frequency | percentage | total frequency |
| 74.7 | 75.4 | IIIIII | 6 | 0.2 | 20 | 20 |
| 75.5 | 76.1 | IIIIII | 6 | 0.2 | 20 | 40 |
| 76.2 | 76.8 | IIIIII | 4 | 0.133333333 | 13.33333333 | 53.333333 |
| 76.9 | 77.5 | IIIII | 3 | 0.1 | 10 | 63.333333 |
| 77.6 | 78.2 | IIII | 5 | 0.166666667 | 16.66666667 | 80 |
| 78.3 | 78.9 | III | 6 | 0.2 | 20 | 100 |
| 30 | 1 | 100 |
Histogram
Box plot
| descriptive statistics | |
| mean | 76.8 |
| median | 76.75 |
| mode | 78.8 |
| variance | 1.968966 |
| Standard dev | 1.403198 |
| 5-point summary | |
| minimum | 74.7 |
| lower quartile | 75.55 |
| median | 76.75 |
| upper quartile | 78.025 |
| maximum | 78.9 |
The skewness value is 0.043085744 hence the dataset is slightly skewed to the right. Since the value is not large, mean and median can be used interchangeably to describe the data. However, median describe the data best as mean is slightly dragged in the direction of the skew.
The population in the United States have taken up measures to improve their well-being such as adaptation of healthy lifestyle and improved medical care. It is then expected that the life expectancy will rise up and it has been showcased in the dataset above. As years pass, the life expectance level also rise.
Part II
Age-adjusted death rates; data set as a scatter plot including the best line
Regression line y=mx+b
Average Life Expectancy (Years) = 91.17072-0.01676(Age-adjusted Death Rate)
m=-0.01676; it implies that for every unit additional death rate, one can expect on average a decrease of 0.01676 years in life expectancy.
b=91.17072; it is the life expectancy in years when the death rate is zero.
The correlation coefficient
r=-0.99318, the linear relationship between age adjusted death rate and life expectancy is strongly negative. It is strong since it is close to -1 which is the lowest limit in the correlation coefficient range. This implies that when one the variable increase, the other one decrease.
Coefficient of determination
R-squared=0.986405,
98.64% of the life expectancy variable can be explained by the age-adjusted death rates for the years 1985 to 2014. The high score imply that other variables that influence life expectancy only compose of 1.36% which is very low.
The relationship between age adjusted death rate and life expectancy is linear and can be described through the regression equation; Average Life Expectancy (Years) = 91.17072-0.01676(Age-adjusted Death Rate). It aligns with the expectation that when the death rates are high at any age, then the years of life expectancy will most probably decline. It is supported by the strong, negative correlation coefficient of -0.99 that indicated the close association and the R-squared value that imply the variation of life expectancy explained by the age adjusted death rate.
Life expectancy is projected to change from one year to another. In part I of the paper, a dataset of life expectancy statistics over the years between 1984 and 2014 were analyzed. The minimum years were 74.7years, recorded in 1985 and 1986 while the maximum, 78.9 years, was recorded in 2014. Over the 30 years, the life expectancy rose up exhibiting an upward trend. The outcomes on measures of central tendency were mean (76.8), median (76.75) and mode (78.8). Life expectancy have a correlation coefficient of -0.99 with age adjusted death rates. A negative linear relationship between the two is summarized in the regression equation; Average Life Expectancy (Years) = 91.17072-0.01676(Age-adjusted Death Rate). Whenever the rate decrease by one unit, the life expectancy increase by 0.01676years. It is clear from the coefficient of determination that the age adjusted death rate adequately explain life expectancy at 98.4%.
Reference.
NCHS – Death rates and life expectancy at birth – Data.gov. (2018). Catalog.data.gov. Retrieved 27 March 2018, from https://catalog.data.gov/dataset/age-adjusted-death-rates-and-life-expectancy-at-birth-all-races-both-sexes-united-sta-1900