Topic 6: Statistics

6.1 Discrete data: can be counted Continuous data: can be measured # of heads when flipping a coin # of red cars in a parking lot Continuous data: can be measured Weight, height, time Express continuous data to a sig. fig.

Together P. 285 #1

6.2 Frequency Tables and Polygons Keep track of how often a value occurs discrete

Example 60 students from grade 9 are asked to pick a number between 0 and 4. The result is shown here. Represent the information in a frequency table. 1 4 3 3 4 0 2 2 1 3 3 4 0 4 3 4 3 2 0 1 2 3 4 3 3 0 3 4 2 0 1 2 3 3 4 1 0 3 4 2 0 3 4 4 2 3 3 1 0 4 2 3 2 4 1 0 3 4 3 2

Frequency Polygons Continuous data Line graph Draw it on GDC

Example Time (t min.) Frequency 3 42 6 23 9 8 12 5 15 18 4 21 24 2 27 The table shows the time, in minutes to the nearest three minutes, of 100 telephone calls made from the same cell phone in one month. Draw a frequency polygon. GDC

Grouped Data and Continuous Data Use histograms and stem plots to group data Useful when the data has a wide spread Use for discrete or continuous

Example A survey was carried out in a shopping mall to find out how old people were when they passed their driving test. 150 people between the ages of15 and 92 were interviewed and the results are in the table. Why would grouping this data be a good idea? Age (x) Frequency 15≤ x < 25 85 25≤ x < 35 33 35≤ x < 45 14 45≤ x < 55 8 55≤ x < 65 3 65≤ x < 75 34 75≤ x < 85 2 85≤ x < 95 1

Mid-interval Values Find by summing end values and dividing by 2 Ex. 15 +25 = 40 ÷ 2 = 20

Upper and Lower Boundaries Discrete Lower value in class interval = lower boundary Upper value = upper boundary Continuous Calculate by averaging upper value of one group with lower value of next group

Example Using the table find the upper boundary of first interval. What is the lower boundary for the second interval? What would the intervals now look like? Age Frequency 0-9 8 10-19 12 20-29 15 30-39 6

Frequency Histograms Visual way to represent data Equal class intervals No space between bars Label axes. Look at p. 288 Frequency Histogram

Stem and Leaf Diagram Orders the data One digit behind stem Provide a key Ex. 12 5 = 12.5

Example These are the times taken (in minutes) for 50 batteries to run out. 450 451 453 455 462 465 466 469 470 470 477 478 483 484 485 488 489 489 491 495 495 498 500 501 502 504 504 505 506 508 508 511 511 513 514 517 519 521 522 536 537 539 541 544 544 546 547 548 548 Construct a stem and leaf diagram

Back-to-back stem and leaf diagram Look at page 289 Assignment: p. 289-290 #1, 3, 4,5,6, 7, 8