Unit 2: Descriptive Statistics 6D Quantitative Continuous Data, 6E Measure of Center from Other Sources Unit 2: Descriptive Statistics 6D, 6E 2/24/2019 8:21 PM

Quantitative Continuous Data usually based on measurements quality of data depends on the device and process used to measure no two data values are exactly the same does not make sense to use frequencies for individual datum (e.g.: mode) need to group into class intervals of equal width using a frequency table 6D, 6E 2/24/2019 8:21 PM

Organizing Quantitative Continuous Data 1. Decide on the number of class intervals. (generally 5 to 20) n: quantity of data 2. Find the class width. Round to the same level of precision as the original data, but always round up. 3. Make the minimum value the lower class limit for the first class. Add the class width to obtain the remaining lower class limits. 4. Use the lower class limits to determine the upper class limits. 5. Use tally marks to determine frequencies for the classes. 6D, 6E 2/24/2019 8:21 PM

Grouped (Class Intervals) Copy For the mean use the midpoint: mean of a class interval’s endpoints assumes the scores within each class are evenly distributed calculated mean is an approximation of the true mean For the mode modal class: class which occurs most frequently For the median median: find the median interval (interval in which the median lies) L: lower boundary of median class i: number of scores in the median class needed to arrive at the median score f: number of scores in the median class C: length of the class interval (class width) 6D, 6E 2/24/2019 8:21 PM

Describing Data A sample of 20 juvenile lobsters was randomly selected from a tank containing several hundred. The length of each lobster was measured in cm, and the results were: 4.9 5.6 7.2 6.7 3.1 4.6 6.0 3.7 7.3 6.0 5.4 4.2 6.6 4.7 4.4 3.6 4.2 5.4 5.0 5.8 Organize the data using a frequency table, and hence graph the data in a histogram. 6D, 6E 2/24/2019 8:21 PM

Grouped (Class Intervals) Copy How can it be done using a calculator? Length Frequency (f) Midpoint (x) [3.05, 3.95) 3 3.5 [3.95, 4.85) 5 4.4 [4.85, 5.75) 5.3 [5.75, 6.65) 4 6.2 [6.65, 7.55) 7.1 TOTAL 20 Length Frequency (f) 3.1 – 3.9 3 4.0 – 4.8 5 4.9 – 5.7 5.8 – 6.6 4 6.7 – 7.5 TOTAL 20 Length Frequency (f) Midpoint (x) f x x [3.1, 4.1) 3 3.6 10.8 [4.1, 5.1) 7 4.6 32.2 [5.1, 6.1) 6 5.6 33 [6.1, 7.1) 2 6.6 13.2 [7.1, 8.1) 7.6 15.2 TOTAL 20 106 6D, 6E 2/24/2019 8:21 PM

Example A school has conducted a survey of 60 students to investigate the time it takes for them to arrive to school. The following data gives the travel times to the nearest minute. 12 15 16 8 10 17 25 34 42 18 24 18 45 33 38 45 40 3 20 12 10 10 27 16 37 45 15 16 26 32 35 8 14 18 15 27 19 32 6 12 14 20 10 16 14 28 31 21 25 8 32 46 14 15 20 18 8 10 25 22 a. Is time discrete or continuous? b. Construct a frequency table for the data using class intervals 0< t < 10, 10 < t < 20, …, 40 < t < 50. c. Draw a histogram to represent the data. d. Describe the distribution of the data. e. What is the modal traveling time? 6D, 6E 2/24/2019 8:21 PM

Practice p. 169: 2, 5, 6 p. 173: 6 p. 178: 2, 4 p. 181: 2, 3, 6 Read and follow all instructions. List the page and problem numbers alongside your work and answers in your notes. Use the back of the book to check your answers. Copy 6D, 6E 2/24/2019 8:21 PM