Managerial Report - Essay Example

Managerial Report This report aims at evaluating the parameters describing 100 counties. Four parameters are analyzed in the report: median household income, average years of schooling, average lifespan and average number of people per household. The report will estimate the descriptive statistics related to each parameter. The report will further find the outliers for each variable. The paper will then estimate the relationship between the median household income and three remaining variables. The conclusion about the parameters’ descriptive statistics and the relation between the parameters will be made. Managerial Report Introduction The economy, the social life and the satisfaction with life can be estimated using the statistical analysis of the corresponding data. The analysis permits to find the mean value of the parameter and to estimate whether the difference between the mean value and the particular measurement is due to the effect of the certain factor or whether it is within the confidence limit for the estimated parameter. The statistical analysis permits also to estimate the hidden trends and relationship between the parameters (Mendenhall, Beaver and Beaver, 2013). The aim of this analysis is to estimate the parameters related to the economy, demography and social life of the countries. The data from 100 counties represents the information about the following indices: average lifespan, average number of people per household, median household income and average number of people per household. The provided data permits to estimate each parameter, as well as the relationship between them. Descriptive Statistics The analysis is started from the estimation of each variable. The Data Toolkit in Excel is used for this purpose. To obtain the descriptive statistics for each parameter the option “Descriptive Statistics” is chosen in the Data Toolkit. The obtained table provides information about the mean, median, mode, range and other main parameters of the descriptive statistics (Anderson, Sweeney, Williams, Camm and Cochrane, 2015). The information and its analysis are given below. Median household income in dollars   Mean 47161,07 Standard Error 796,3485093 Median 46775 Mode - Standard Deviation 7963,485093 Sample Variance 63417094,83 Kurtosis -0,696577768 Skewness 0,25354131 Range 37750 Minimum 34050 Maximum 71800 Summ 4716107 Count 100 The descriptive statistics for the median household income shows that there is a significant difference between maximum and minimum value of this index. The minimum value is more the two times less from the maximum value. The data is distributed symmetrically because the mean and the median are very close and the skewness is comparatively small. It can be assumed that the data is normally distributed (Mendenhall, Beaver and Beaver, 2013). The main feature of the data is the large difference between the maximum income ($ 7,180) and the minimum income ($ 34050), as well as corresponding large range. The data about the average years of schooling show that in most counties people study about 12 years. The close values of the mean, mode and median is a sign that this situation is typical for most of the counties. The data is also symmetrical and normally distributed. The minimum value of 9.9 years may mean that the small number of people decide to enter college or even do not graduate from high school. The maximum value of 14 years means that most of people in the county continue their education after the high school. However, the most typical situation is that about a half of population or lees decides to continue the education in the college or university. Average years of schooling   Mean 12,092 Standard Error 0,090438662 Median 12,1 Mode 11,7 Standard Deviation 0,904386616 Sample Variance 0,817915152 Kurtosis -0,196804081 Skewness -0,091331665 Range 4,1 Minimum 9,9 Maximum 14 Summ 1209,2 Count 100 The data about the average lifespan show that there is a significant difference between the maximum and the minimum value of this parameter. However, the values of mode and median are median are close, which means that the average lifespan for the most counties is 77-78 years. The fact that the mean value is less than mode and median can be explained by the presence of the outliers or the counties, where the average lifespan is significantly lower than the average value. Average lifespan in years   Mean 76,809 Standard Error 0,242504171 Median 77,15 Mode 78,1 Standard Deviation 2,425041705 Sample Variance 5,880827273 Kurtosis -0,831881119 Skewness -0,285031034 Range 10,6 Minimum 70,3 Maximum 80,9 Summ 7680,9 Count 100 The table of descriptive statistics for average number of people per household show that the data is normally distributed. The mean, median and mode are very close to each other. The minimum value of 1.8 persons per household means that children prefer to live separately from the parents in most families of the county. The maximum value of 3.5 persons per household means that children and parents share one household or old parents live together with their grown children. The most typical situation is when 2-3 people live in one household. Average number of people per household   Mean 2,565 Standard Error 0,04130143 Median 2,6 Mode 2,7 Standard Deviation 0,413014295 Sample Variance 0,170580808 Kurtosis -0,734062504 Skewness -0,021582865 Range 1,7 Minimum 1,8 Maximum 3,5 Summ 256,5 Count 100 Outliers The presence of outliers or the data that differs significantly from the rest can be estimated using the z-score. The z-score for the individual value is calculated using the following formula (Mendenhall, Beaver and Beaver, 2013): where x is an individual value of the variable; μ is the population mean; and σ is the standard deviation. The calculation of z-score for the individual values are given below. Z-score shows how far (using the standard deviation scale) the individual value is located from the mean value. If the confidence level of 95 % is chosen, 95 % of data will have the z-score between -1.96 and 1.96. The outliers will have z-score less than -1.96 or greater than 1.96 (Anderson, Sweeney, Williams, Camm and Cochrane, 2015). The found outliers for each variable are given in the tables below. The variable median household income has only one outlier. It is the county Collin where the median income is $ 71,800. Z-score is 3.094, which means that this value is more than 3 standard deviations greater than the mean value. It may mean that the work in this county is paid or there can be a factor affecting the increase of the salaries. The analysis of outliers for the variable average years of schooling shows that there are three counties where people study more than in the rest counties. In three counties people study less than in the rest of counties. It also means that the specific factors may affect the attitude to education in these counties encouraging them to get additional education or not. County z-score Average years of schooling Ballard 2,110619 14 Benewah 2 13,9 Borden 2,110619 14 Cone -2,42478 9,9 Cotton -2,09292 10,2 Sullivan -2,31416 10 Concerning the variable average lifespan, this parameter is the lowest in two counties. It can be explained by the presence of factor that affects health state of the people in these counties. The other explanation can be the lifestyle, which could be unhealthy. County z-score Average lifespan in years Concho -2,68412 70,3 Delaware -1,98309 72 As for the variable average number of people per household, the results for two counties can be treated as the outliers. The parameter is higher than the average value. The presence of such a factor as regional tradition of living in big family may be the explanation for this fact. It must also be admitted that the county Concho is the outlier for two variables. The lowest average lifespan and the highest average number of persons per household are detected for this county. County z-score Average number of people per household Concho 2,263923 3,5 Denton 2,021792 3,4 Relationship between the Parameters The relationship between the variables can be estimated by the graphs (scatterplots) showing the dependency of one variable from the other. To estimate the relationship, the trend line is added on the scatterplot using the option in the menu Diagram in Excel. The options of showing the equation and the value of the coefficient of determination R2 are also chosen. The square root of R2 gives the value of the correlation coefficient R. The closer is the value of R to 1, the stronger is the relationship (or correlation) between the variables (Anderson, Sweeney, Williams, Camm and Cochrane, 2015). The graph below shows the relationship between the median household income and average years of schooling. It is seen from the graph that these variables are strongly correlated. R2 = 0.801 and the correlation coefficient is R = = 0.89. The scatterplot supports the statement the income depends on the years of schooling. The better education a person gets the higher is probability that he (she) will get a highly paid job. The average lifespan and median household income can also be connected. It is supposed that the persons that have higher income will have the higher average lifespan. The explanation can be the better living condition and access to the better medical care. The graph below supports this statement. It shows that above mentioned parameters are strongly correlated. R2 = 0.7377 and the correlation coefficient is R = = 0.86. The median household income and average number of people per household are not correlated. The scatterplot does not show the significant relationship between these parameters. The coefficient of determination R2 = 0.0104. Thus, R = = 0.102. The absence of the relationship can be explained by the fact that each person in the family is employed and the salary of the family members does not differs significantly. The relationship could exist if only one family member would be employed and would earn money for the whole family. Conclusion The conducted analysis shows that all estimated variables are normally distributed. The average values for the variables average number of people per household, average lifespan and average years of schooling are close to the corresponding modes, which means that the mean values of these variables represent the most typical value of the parameter. The variable median household income has the highest range. The variable average lifespan has the second highest range. Each variable has outliers. The most outliers are found for the variable average years of schooling. 3 counties have the values less than average, and 3 counties have values higher than mean. Both variables average lifespan and average number of people per household have two outliers. The variable median household income has one outlier. The presence of outliers mean that the particular factor existing in the county may affect the parameter resulting in its increase or decrease. The variables average lifespan and average years of schooling are strongly correlated with the variable median household income. The median household income is positively correlated with average years of schooling. The average lifespan is positively correlated with median household income. The relation between median household income and average number of persons per household was not found. References Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm, J.D., & Cochrane, J.J. (2015). Essentials of statistics for business and economics (7th ed.). Mason, OH: South-Western Cengage Learning. Mendenhall, W., Beaver, R. & Beaver, D. (2013). Introduction to Probability and Statistics, Boston, MA: Brooks/Cole, Cengage Learning. Read More