Bivariate numerical data #1 - Questions and Answers

Question 1 You were asked about advantages of using box plots and dot plots to describe and compare distributions of scores. Do you think the advantages you found would exist not only for these data, but for numerical data in general? Explain. Answer Yes, because box plot and dot plot can be used both for numerical data. However, dot plot is used for relatively small data while box plot can be used with large number of data. Dot plots display cluster or gaps of data while box plot shows the range and distribution of data along a number line. Question 2 Differentiate between univariate, bivariate and multivariate data. Answer Univariate data: A data set with only one variable under study is referred to as a univariate data set. Bivariate data: Bivariate data are those that include two variables being studied simultaneously. Multivariate data: Multivariate data is defined as data, which consists of more than two variables under study, simultaneously. Example: Consider a data set with 𝑛 n individuals. Suppose that only one characteristic of each individual is studied. Then, the data would record only one variable for each sampled individual. In this case, the data would be a univariate data. Now, suppose that two characteristics of each individual are studied simultaneously. Then, the data would record two variables for each sampled individual. These two variables would be dependent on each other, as they are collected from the same individual. In this case, the data would be bivariate data. Again, suppose that three or more characteristics of each individual are studied simultaneously. Then, the data would record three or more variables for each sampled individual. These variables would be dependent on each other, as they are collected from the same individual. In this case, the data would be a multivariate data. Question 3 To find: The qualitative or quantitative and as univariate or bivariate. Answer Given information: Monthly low temperatures in Rochester, New York. Calculation: Consider the question: Here, monthly low temperatures in Rochester, New York. Quantitative: The data to represent the temperature has the numerical value and temperature is measured in unit like Celsius, Fahrenheit. Quantitative data: the data which describes the numerical value or quantities is said to be quantitative. The data has the numerical value and numerically compared. The data for temperature is represented by only one variable number. Therefore, for any variable 𝑛 n such that 𝑛 = 1 , 2 , 3 , . . . 𝑛 n=1,2,3,...n. There is only one variable which represent the low in temperature. The data monthly low temperatures in Rochester, New York data is univariate. Therefore, the monthly low temperatures in Rochester, New York is quantitative and univariate. Question 4 To explain: The shape of the new distribution and the measure of center and variation affected in a given data. Answer Given: A data set is a symmetric distribution. Every value in the data set is doubled. Concept used: Bivariate joint frequency distribution are contingency table. The total row and total column of the marginal distribution while the body of the table is the joint frequencies. Calculation: The height will be doubled but will still be symmetric. Each value in a numerical data set is multiplied by a real number 𝑘 k where 𝑘 > 0 k>0. The measures of center and variation is founded by multiplying the original measures by 𝑘 k. Therefore: This is also doubled. Question 5 When working with bivariate data, which of these are useful when deciding whether it’s appropriate to use a linear model? The scatterplot The residuals plot The correlation coefficient Options: (A) I only (B) II only (C) II only (D) I and II only (E) I, II, and III Answer Step 1: Scatterplot: A scatterplot is a type of data display that shows the relationship between two numerical variables. Each member of the data set gets plotted as a point whose ( 𝑥 , 𝑦 ) (x,y) coordinates relates to its values for the two variables. Step 2: Residual plot: A residual plot is a graph that may plot the residual (or the difference between the observed and predicted value of the response variable) against each predictor variable or against the predicted values of the response variable, according to need. Step 3: Correlation coefficient: Correlation is a measure which indicates the “go-togetherness” of two data sets. It can be denoted as 𝑟 r. Answer: 𝐼 , 𝐼 𝐼   and   𝐼 𝐼 𝐼 . I,IIandIII.