1. 1.1 Constructing and Interpreting Visual Displays of Data Number of Pirates CityFrequency Waterloo100 Kitchener200 Cambridge50 100110120130140150160170180 There are a surprising number of pirates in the local area. The most pirates are in Kitchener. Cambridge pirates are generally short. = 50 pirates

2. Example 1 Number of Pirates CityFrequency Waterloo100 Kitchener200 Cambridge50 Imagine that only 10,000 people in the three cities were studied to gather the data. Identify the population, data, & sample. The population is all people living in Kitchener, Waterloo and Cambridge. The data is number of pirates found in each city (100, 200 and 50) The sample is the 10,000 people who were studied.

3. Example 2 Calculate the angles for the pie graph corresponding to the data. Number of Pirates CityFrequency Waterloo100 Kitchener200 Cambridge50 Total = 350 Waterloo: 100 / 350 = 0.285… x 360 =102.9 Kitchener: 200 / 350 = 0.571… x 360 = 205.7 Cambridge: 50 / 350 = 0.142… x 360 = 51.4

4. Example 3 Is this a bar graph or a histogram? This is a histogram because the data is continuous. This means that every possible number including decimals can be represented with the data. 100110120130140150160170180 A corresponding bar graph might look something like this. What are the class intervals? 100 – 109.99…., 110 – 119.99 …, 120 – 129.99 …, etc 100 – 110, 110 – 120, 120 – 130, etc is an acceptable answer. Just realize that the second number in each interval is not included.

5. Example 4 Create a box and whisker diagram for the height data. STEP 1: Find the median (middle value) of the data 50 data values, the middle is the average of 25 th and 26 th Both are in 120 – 130. Assume they are both 125. Therefore the median is 125 STEP 2: Find the medians of the bottom half and top half 25 data values in each half. Need the 13 th in each half. 13 th value in the bottom half is in 110 – 120 … assume 115 13 th value (38 th overall) in the top half is in 130 - 140 … assume 135 STEP 3: Draw it Height of Pirates IntervalFrequency 100-1105 110-12010 120-13015 130-14010 140-1505 150-1602 160-1702 170-1801 100110120130140150160170180

6. Height of Pirates IntervalFrequency 100-1105 110-12010 120-13015 130-14010 140-1505 150-1603 160-1702 170-1801 Technically I “cheated” to find the medians. The “cheating” may will get you a 4- only. Here is the proper way … its complicated Median is average of 25 th and 26 th piece of data … Need 10 th and 11 th in 120 – 130 and there are 15 numbers in the interval and the interval is 10 units long. 10 / 15 = 0.666... X 10 = 6.66 + 120 = 126.66 11 / 15 = 0.733 … X 10 = 7.33 + 120 = 127.33 Average of 126.66 and 127.33 is 127 (instead of 125) Bottom half median is 13 th piece of data Need 8 th in 110 – 120 and there are 10 numbers in the interval and the interval is 10 units long. 8/10 = 0.8 x 10 = 8 + 110 = 118 Median of the bottom half is 118 (instead of 115) Top half median is 38 th piece of data Need 8 th in 130 – 140 and there are 10 numbers in the interval and the interval is 10 units long. 8/10 = 0.8 x 10 = 8 + 130 = 138 Median of the bottom half is 138 (instead of 135)

7. Important Facts Your homework is: Read: Pg 3 – 10 and Do: Pg 11 # 2, 4 -10 population, sample, class interval, median are important terms 6 types of charts/graphs appeared in the lesson there are 2 other types to know as well. The only two that require any calculations are pie graph, box and whisker Make sure you can do the calculations Pirates are very interesting