MATH113: First Midterm Review Page
The first midterm exam covers material from page 712 through page 794
of the textbook with the exception of the use of z-scores (section 13.3). The objectives covered are listed below with a few sample problems for each one.
To get a feel for Professor Burgiel's test writing style, you can look at her MATH112 final and her quizzes and sample final for MATH130.
This exam will cover the objectives listed below. Sample problems are given for each objective.
Understand and use descriptive statistics:
Understand and apply basic concepts of probability:
- Use measures of central tendency (mean, median, mode) and range to describe and interpret real world data.
- The scores on the first quiz were 100, 95, 90, 85, 90, 95, 100, 100, 100 and 90. Find the mean and standard deviation of the quiz scores.
- True or false: in any data set, at least half of the data lies above the mode of the data set.
- Use a bar and whisker plot to fill in the blank: "Three quarters of the students in Mrs. Connor's class were over _______ in height."
- Select appropriate ways to present data in communicating statistical information (e.g. tables, graphs, line plots, Venn diagrams).
- The table below
gives the size of the freshman class entering BSC for the past several
Would a pie chart be an appropriate way of displaying this data? Why or why not?
What is the best way of graphically displaying this data, and why? (There may be more than one correct answer to this question.)
- Analyze and interpret graphic and non-graphic data representations (e.g. frequency distributions, percentiles).
- Use the graph on page 722 to estimate the size of the sheep population in 1970.
- Use the histogram on page 753 to estimate the proportion of male students over 70.5 inches in height.
- Compare different data sets.
- The table below lists the median, lower quartile an upper quartile of the scores of two different exams. Write a grammatically correct paragraph describing the similarities and differences between the two exams.
- Two tests were given to the same group of students; the resulting test scores were normally distributed. On the first test, the mean was 90 and the standard deviation was 10. On the second test the mean was 95 and the standard deviation was 5.
On which test did more students score above 100, or did both tests have about the same number of students scoring over 100? Explain your reasoning.
On which test did more students score below 80, or did both tests have about the same number of students scoring below 80? Explain your reasoning.
Approximately what proportion of students scored between 80 and 100 on the first test?
- Calculate experimental probabilities of simple and compound events and of independent and dependent events.
- Suppose you're given a frequency histogram describing the outcome of rolling a pair of dice and adding their values. Calculate:
The probability of rolling a 7.
The probability of rolling an even number.
The probability of rolling a 2 or a 12.
The probability of rolling an even number or a number greater than 7.
The probability of rolling a 6 and then rolling again and getting another 6.
- Use the histogram on page 753 to estimate the probability of a male student selected at random having a height of under 66.5 inches.
- Demonstrate knowledge of counting, combinations and permutations.
- A bag contains 4 red balls and 2 blue balls. Draw a possibility tree and calculate the number of ways of drawing one red and then one blue ball.
- A bag contains 4 red balls and 2 blue balls. Draw a possibility tree and calculate the number of ways of drawing one red and one blue ball, in either order.
- The math club has ten members. How many different ways are there to elect a president, a vice president, and a treasurer for the club?
- The math club has ten members. How many different ways are there to form a committee of 4 members?
- The math club has ten members; three plan to be actuaries and 7
plan to be teachers. How many different ways are there to form a
committee of 3 future teachers and one future actuary?