Online test, 40 mins, 5 to 8 questions, topic is statistics.
Math 123 Fall 2017 Dr. Lily Yen Assignment 3 Show all your work Name: Number: Signature: Score: /20 Problem 1: Below is a list of ages of 30 people in Kamloops who volunteered to help victims of wild fire in BC this summer. 60, 69, 72, 62, 57, 66, 55, 69, 66, 72, 51, 74, 70, 58, 58, 53, 68, 53, 55, 53, 53, 59, 57, 51, 72, 65, 51, 60, 70 and 64. a. Make a stem-and-leaf plot of the data. 5 7 5 1 8 8 3 3 5 3 3 9 7 1 1 6 0 9 2 6 9 6 8 5 0 4 7 2 2 4 0 2 0 b. Construct a relative frequency table using five classes. Age Frequency Relative frequency 51–55 9 0.300 56–60 7 0.233 61–65 3 0.100 66–70 7 0.233 71–75 4 0.133 Total 30 c. Draw a histogram from your relative frequency table. Clearly label the axes. Age R el at iv e fr eq u en cy 50 55 60 65 70 75 0.1 0.2 0.3 Score: /6 Problem 2: In our class of 21, suppose 10 drive to Cap, 8 take public transit, and 3 walk. Draw a pie chart for the above data. Include your steps for the calculation of each sector angle in the pie. Freq. Rel. freq. Angle Drive 10 0.476 171 Transit 8 0.381 137 Walk 3 0.143 51 Total 21 Drive Transit Walk Score: /3 Problem 3: Below is a list of 21 ages of the students from one of Lily’s classes. 20, 19, 22, 22, 27, 26, 25, 19, 26, 22, 21, 24, 20, 18, 18, 23, 18, 23, 45, 33 and 43. Construct a box-and-whisker plot by computing the median, first and third quartiles com- plete with the minimum and the maximum. Min 18 1st Quartile 19.8 Median 22 3rd Quartile 26 Max 45 Mean 24.5 Mode 18, 22 20 25 30 35 40 45 Score: /5 Problem 4: Using the same age data from the previous problem, compare its mode, mean, and median. Score: /2 Problem 5: The grade assignment on the curve is shown below where µ is the mean and s is the sample standard deviation. µ− 3 2 s µ− 1 2 s µ µ+ 1 2 s µ+ 3 2 s F D C B A 66.0 76.8 82.2 87.6 98.4 Suppose the final marks in a class of ten students are 80, 76, 81, 94, 79, 60, 85, 100, 75 and 92. What grade does the person earning 79 get? The mean is µ = 82.2 and the standard deviation is σ = 10.8. That leaves the ranges indicated in the figure above. A 79 therefore earns a C. Score: /4 Page 2 Math 123 Math 123 Fall 2017 Dr. Lily Yen Assignment 3 Show all your work Name: Number: Signature: Score: /20 Problem 1: Below is a list of ages of 30 people in Kamloops who volunteered to help victims of wild fire in BC this summer. 60, 69, 72, 62, 57, 66, 55, 69, 66, 72, 51, 74, 70, 58, 58, 53, 68, 53, 55, 53, 53, 59, 57, 51, 72, 65, 51, 60, 70 and 64. a. Make a stem-and-leaf plot of the data. 5 7 5 1 8 8 3 3 5 3 3 9 7 1 1 6 0 9 2 6 9 6 8 5 0 4 7 2 2 4 0 2 0 b. Construct a relative frequency table using five classes. Age Frequency Relative frequency 51–55 9 0.300 56–60 7 0.233 61–65 3 0.100 66–70 7 0.233 71–75 4 0.133 Total 30 c. Draw a histogram from your relative frequency table. Clearly label the axes. Age R el at iv e fr eq u en cy 50 55 60 65 70 75 0.1 0.2 0.3 Score: /6 Problem 2: In our class of 21, suppose 10 drive to Cap, 8 take public transit, and 3 walk. Draw a pie chart for the above data. Include your steps for the calculation of each sector angle in the pie. Freq. Rel. freq. Angle Drive 10 0.476 171 Transit 8 0.381 137 Walk 3 0.143 51 Total 21 Drive Transit Walk Score: /3 Problem 3: Below is a list of 21 ages of the students from one of Lily’s classes. 20, 19, 22, 22, 27, 26, 25, 19, 26, 22, 21, 24, 20, 18, 18, 23, 18, 23, 45, 33 and 43. Construct a box-and-whisker plot by computing the median, first and third quartiles com- plete with the minimum and the maximum. Min 18 1st Quartile 19.8 Median 22 3rd Quartile 26 Max 45 Mean 24.5 Mode 18, 22 20 25 30 35 40 45 Score: /5 Problem 4: Using the same age data from the previous problem, compare its mode, mean, and median. Score: /2 Problem 5: The grade assignment on the curve is shown below where µ is the mean and s is the sample standard deviation. µ− 3 2 s µ− 1 2 s µ µ+ 1 2 s µ+ 3 2 s F D C B A 66.0 76.8 82.2 87.6 98.4 Suppose the final marks in a class of ten students are 80, 76, 81, 94, 79, 60, 85, 100, 75 and 92. What grade does the person earning 79 get? The mean is µ = 82.2 and the standard deviation is σ = 10.8. That leaves the ranges indicated in the figure above. A 79 therefore earns a C. Score: /4 Page 2 Math 123 chapter-statistics-qdxecysr.pdf july19math123-0vge03ab.pdf Example According to US government statistics, mononucleosis (mono) is four times more common among college students than the rest of the population. Blood tests for the disease are not 100% accurate. Assume that Table 13.2 was obtained regarding students who came to Capilano’s health centre complaining of tiredness, a sore throat, and slight fever. Has Mono No Mono Total Positive test 72 4 76 Negative test 8 56 64 Total 80 60 140 Table 13.2: Test results for mononucleosis Find the probability the student does not have mono, given that the test is positive. Practice exercises in Section 13.3: Every second odd from 1–59. 80 Lily Yen Text Box Distinguish between disjoint (mutually exclusive) events and independent events. Chapter 14: Descriptive Statistics 14.1 Organizing and Visualizing Data Definition Statistics is the science of planning studies and experi- ments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data. A common and important goal of is to learn about a large group by examining data from of its members. For this purpose, we need the following terms: Terminology: 1. A population 2. A census 3. A sample 4. Data 81 Lily Yen Text Box 7:00 Lily Yen Text Box statistics Lily Yen Text Box a subset Lily Yen Text Box the entire collection of subjects under study Lily Yen Text Box is the study of entire population Lily Yen Text Box is a subset of the population, unbiasedly chosed Lily Yen Text Box a collection of information: there are two types, 1) qualitative, like hair colour, or ethnicity or make of car 2) quantitative, numerical information We learn to construct and interpret frequency tables of two types: 1. single value categories 2. grouped frequency tables Definition A frequency distribution or frequency table shows how a data set is partitioned among all of several categories (or classes) by listing all of the categories along with the number of data values in each of the categories. Example Let us conduct a survey of the number of buses each student needs to take to come to Capilano University in our class. Now we organize it in a frequency table, i. e. for each category (n buses), we count the number of students who take n buses for n = 0, 1, 2, 3, · · · . (See steps after example 2.) 82 Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Lily Yen Example Let us survey our class for height in centimetres, then organize our data according to the steps above. Let us first gather all heights. Below, we construct a table in five columns with the following heading: height (cm), tally, frequency, (and relative frequency, and cumulative frequency for later). Follow guidelines below for a frequency table. When you construct a frequency distribution to summarize a large data set, the following steps can be helpful: 1. Determine the number of classes