1. Qualitative vs. Quantitative & Displaying Data

2. “There are three kinds of lies: lies, damned lies, and statistics.” –Benjamin Disraeli (1804-1881) & popularized by Mark Twain (1835-1910)

3. -Population: a defined collection of individuals or objects about which we want to draw conclusions; the whole group from which we may collect data -Census: the collection of information from the whole population -How often does the US do a census? -Is it always possible, or even necessary, to access data for an entire population? -What might we do instead?

4. -Sample: a subset of the population from which we want to collect information; a small group chosen from the population -How could we determine who/what to include in the sample? -Random sample: a sample where each element has the same chance of being included -Biased sample: a sample that is not random

5. 1. Brett wants to find out if there is a connection between eating breakfast & grades earned among students at his school. However, there are too many students in the school to ask everyone. He needs to pick a sample. How can Brett make sure his sample is random? 2. Catherine is conducting a survey to find out how much money women who live in New York spend on fashion in a month. She interviews women coming out of Neiman Marcus. Is this a random sample?

6. The 1936 Literary Digest Poll -Presidential election of 1936: Alfred Landon (Republican governor of Kansas) vs. Franklin D. Roosevelt (incumbent President) -1936 marked the end of the Great Depression, and economic issues such as unemployment and government spending were the dominant themes of the campaign -Literary Digest was one of the most respected magazines of the time and had a history of accurately predicting the winners of presidential elections that dated back to 1916

7. The 1936 Literary Digest Poll Literary Digest’s prediction Landon: 57% Roosevelt: 43% Conducted one of the largest and most expensive polls ever, with a sample size of around 2.4 million people Actual outcome Landon: 38% Roosevelt: 62% George Gallup was able to predict a victory for Roosevelt using a much smaller sample of about 50,000 people

8. *If you use sampling in your project, you will need to discuss how you picked your sample. You must prove that your sample is, indeed, random!

9. -Survey: the collection of information from a sample -Is it possible that how we word a survey question impacts how people respond? Do you agree or disagree with the following statement? Teachers should not be required to supervise their students during lunch. -Data: information about individuals in a population -Parameter: a numerical quantity measuring some aspect of a population -Statistic: a quantity calculated from data gathered from a sample; usually used to estimate a population parameter

10. Types of Data -Qualitative/categorical data: describes a particular quality or characteristic; can be put into categories Examples: gender (male, female); video gaming systems (Xbox, PlayStation, Wii, etc.)

11. Types of Data -Quantitative data: has a numerical value -Discrete: data that can only take specific values; can be counted -Examples: number of students in this room; number of candies in a package -Continuous: any value within a range; can be measured -Examples: time taken to run a 100k race; height; weight* *The weighing scale was invented at a time when countries began trading materials and a standard measurement was required to ensure fair trading.

12. Types of Data Qualitative/categorical, quantitative – discrete, or quantitative – continuous? -Religious preference -Number of leaves on a tree -The currencies of the world -Volume of water in a swimming pool -Qualitative/categorical -Quantitative – discrete -Qualitative/categorical -Quantitative – continuous

13. When there is a large amount of data, it is easier to interpret if the data is organized in a table or displayed as a graph.

14. Frequency Table Frequency: how often a value occurs The number of candies in 24 packets are shown below: Organize this information in a frequency table. 222322 232122 20222421 2221222322 2420222322 Number of candiesTallyFrequency 20 21 22 23 24 Number of candiesTallyFrequency 20|| 21||| 22|||| |||| ||| 23|||| 24|| Number of candiesTallyFrequency 20||2 21|||3 22|||| |||| |||13 23||||4 24||2 The tally column is not required, but it is helpful for large data sets.

15. Bar Graph -AKA bar chart or column graph -Used to display qualitative/categorical data or ungrouped discrete data -x-axis: categories of data (qualitative) or range of data values (ungrouped discrete) -y-axis: frequency of data values -Column widths are equal -Include spaces between bars -You must create your bar graph with a straight edge! (Likely worth 1 point on the IB exam)

16. Bar Graph Here’s what a bar graph would look like for our candy frequency table: Number of candies Frequency 202 213 2213 234 242 Number of candies Frequency

17. Bar Graph Construct a bar graph from the following data: Type of transportationBusCarTaxiBikeWalk Frequency76412

19. Grouping It is especially useful to group continuous data. Since we measure continuous data, we can only take measurements that are as accurate as our measuring device. Since no two continuous data values will be exactly the same, it doesn’t make sense to talk about the frequency of a particular piece of continuous data. When we group data, we can instead talk about class intervals of equal width.

20. 3.112.29.68.12.21.215.04.821.213.6 17.322.31.54.631.226.77.818.234.41.6 2.95.512.828.316.91.35.67.82.36.9

21. Grouped Frequency Tables 3.112.29.68.12.21.215.04.821.213.6 17.322.31.54.631.226.77.818.234.41.6 2.95.512.828.316.91.35.67.82.36.9 Length of call (minutes) (t) TallyFrequency 0 ≤ t ˂ 5 5 ≤ t ˂ 10 10 ≤ t ˂ 15 15 ≤ t ˂ 20 20 ≤ t ˂ 25 25 ≤ t ˂ 30 30 ≤ t ˂ 35 Length of call (minutes) (t) TallyFrequency 0 ≤ t ˂ 5|||| 5 ≤ t ˂ 10|||| || 10 ≤ t ˂ 15||| 15 ≤ t ˂ 20|||| 20 ≤ t ˂ 25|| 25 ≤ t ˂ 30|| 30 ≤ t ˂ 35|| Length of call (t minutes) TallyFrequency 0 ≤ t ˂ 5|||| 10 5 ≤ t ˂ 10|||| ||7 10 ≤ t ˂ 15|||3 15 ≤ t ˂ 20||||4 20 ≤ t ˂ 25||2 25 ≤ t ˂ 30||2 30 ≤ t ˂ 35||2

22. Histogram -Used to display grouped discrete or continuous data -x-axis: class intervals -y-axis: frequency of class intervals -Column widths are equal -No spaces between bars -You must create your histogram with a straight edge! (Likely worth 1 point on the IB exam)

23. Histogram Here’s what a histogram would look like for our call length frequency table: Length of call (t minutes) Frequency 0 ≤ t ˂ 510 5 ≤ t ˂ 107 10 ≤ t ˂ 153 15 ≤ t ˂ 204 20 ≤ t ˂ 252 25 ≤ t ˂ 302 30 ≤ t ˂ 352

24. Histogram Construct a histogram from the below data representing length of lobsters: Lobster length (l cm)Frequency 3 ≤ l < 43 4 ≤ l < 56 5 ≤ l < 65 6 ≤ l < 74 7 ≤ l < 82

25. -If we are given a raw set of data, can we determine the lowest and highest data values? -If data values are grouped in classes on a frequency table or column graph, can we determine the lowest and highest data values?

26. Percentages You can use frequency tables or bar charts / histograms to determine specific percentages that apply to the data.

27. Percentages – Frequency Table Number of candies Frequency 202 213 2213 234 242 In IBMS, we always use 3 significant figures (3SFs)!

28. Percentages – Frequency Table Number of candies Frequency 202 213 2213 234 242

29. Percentages – Graphs

31. What percentage of lobsters are exactly 7.5 cm long? Trick question We cannot determine that by looking at the histogram.

32. Describing the Distribution of a Data Set Many data sets show symmetry or partial symmetry about the mode. We call this a symmetrical distribution. Some distributions have been “stretched” to the left or right side. These distributions are called skewed. -Symmetrical distribution-Negatively skewed-Positively skewed -Skewed left-Skewed right