Describe the difference between descriptive statistics and inferential statistics. Use an example to support your answer. 1) Is a random sample all that is needed in order to make a valid statistical inference? 2) Suppose you have a dataset with information on public high schools in Maryland. For each variable listed, determine if the variable is numerical or categorical. If it is numerical determine if it is discrete or continuous. If it is categorical determine if it is nominal or ordinal. a. . Average teacher salary b c d. e. f g h Number of students The race/ethnicity of the principal Number of days the school was closed due to bad weather Whether the school offers a STEM program Student-teacher ratio Number of students on sports teams . A variable ranking the school as above satisfactory, satisfactory, or below satisfactory 3) Consider the following imaginary dataset: m Number of Students Calculate the following descriptive statistics by hand (be sure to show your work): a. Mean b. Variance c. Standard deviation d. Median e. Mode f. Proportion of schools with less than 1000 students 4) Based on your calculations above, is the number of students skewed? If yes, in which direction? How you do you know? 5) Calculate standardized values for the number of students in each school. Interpret the standardized value for school A. 6) Draw a histogram for the number of students in each school using intervals of 500 students. Use a range of 0 to 1500 students