1. 1 Lesson 5.5.1 Evaluating Claims

2. 2 Lesson 5.5.1 Evaluating Claims California Standards: Statistics, Data Analysis, and Probability 2.5 Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims. What it means for you: You’ll look at data intended to support claims and decide if the claim is valid. Key words: claim opinion valid invalid

3. 3 Lesson 5.5.1 Evaluating Claims You’re likely to be bombarded by claims every day. You can only really tell whether a claim is true or not if you examine the evidence. For instance, advertisements often claim that one product is better than another. Claims are presented as facts — but they might not be.

4. 4 A Claim Is a Statement Presented as a Fact Lesson 5.5.1 Evaluating Claims Claims are often reported in newspapers and on television and radio. Claims are different from opinions. A claim is presented as a true fact. An opinion is just someone saying what they believe, such as “I think this brand of cola tastes best.” The average American eats pizza at least once a week. More people choose this toothpaste than any other. In 100 years, there won’t be any glaciers left on Earth. These are examples of claims:

5. 5 Claims Are Often Supported by Data Lesson 5.5.1 Evaluating Claims Data is often used to provide evidence for a claim. You need to look carefully at the data to see if it supports the claim.

6. 6 Example 1 Solution follows… Lesson 5.5.1 Evaluating Claims A grocery-store owner claims that $20 is the amount most often withdrawn from the ATM outside his store during one month. Does this circle graph from the bank’s monthly report, which shows data about that ATM, support his claim? Solution This circle graph does show that the modal amount withdrawn was $20. So the circle graph does support the store owner’s claim.

7. 7 Lesson 5.5.1 Evaluating Claims This doesn’t show that $20 is always the amount withdrawn most often. Next month’s data might be different. So if the store owner had claimed that $20 was always the amount most frequently withdrawn, then you would need to look at more evidence.

8. 8 Example 2 Solution follows… Lesson 5.5.1 Evaluating Claims A different store owner claims that $20 is the mean amount withdrawn from the ATM outside her store during the same month. Does this circle graph from the bank’s monthly report, which shows data about that ATM, support her claim? Solution You need to read the claim very carefully. This time, the claim is that $20 is the mean amount. This can’t be true, since $20 is the smallest amount withdrawn, and all the other amounts will make the mean amount greater than $20. So the circle graph does not support this store owner’s claim.

9. 9 Guided Practice Solution follows… Lesson 5.5.1 Evaluating Claims 1. Is this statement a claim or an opinion? "I think the red team is a better team than the blue team." Explain your answer. An opinion — it doesn’t present this view as a fact. 2. It’s claimed that most families using a swimming pool on a Saturday morning have exactly 2 children. Does the line plot on the right support this claim? 3. Give one example of a claim that would be supported by the line plot. No — most families don’t have 2 children. Ten families have 2 children, while 24 do not have 2 children. For example: more families have 2 children than any other single number.

10. 10 Sometimes the Evidence Is Not Clear Lesson 5.5.1 Evaluating Claims Sometimes, some statistics may support a particular claim, but other statistics will not. One way of doing this is by using a particular measure of central tendency, depending on what claim you want to make. Maybe they want to make the typical value sound high. Or maybe they want to make it sound low. For example, companies make claims to try to persuade you to buy their products. They’ll want to use statistics to make their product look like it’s better than the competitors’. People trying to convince or persuade someone will very often use just the statistics that support their claim. They may ignore statistics that don’t support their claim, or which make their claim look untrue.

11. 11 Example 3 Solution follows… Lesson 5.5.1 Evaluating Claims A newly opened health club wants to attract some new young members. Its current members’ ages are: 25, 25, 37, 45, 53, 54, 55, 57, 63, 67. It wants to advertise, making the claim that the typical age of its current members is low. To achieve this, its advertisement makes the claim that “There are more 25-year-olds at the club than any other age.” Does the data support this claim? Comment on the claim generally. Solution The modal age is 25, so the data does support the claim. And the median age is 53.5. However... the mean age is 10 48125 + 25 +…+ 63 + 67 10 == 48.1. Solution continues…

12. 12 Example 3 Lesson 5.5.1 Evaluating Claims A newly opened health club wants to attract some new young members. Its current members’ ages are: 25, 25, 37, 45, 53, 54, 55, 57, 63, 67. It wants to advertise, making the claim that the typical age of its current members is low. To achieve this, its advertisement makes the claim that “There are more 25-year-olds at the club than any other age.” Does the data support this claim? Comment on the claim generally. Solution (continued) So if the health club had used any other measure of central tendency, the typical age would have sounded a lot higher. Here, the health club wanted to make the typical age of its members sound low in the advertisement, so used the only measure of central tendency that would do this. The club’s claim is not untrue, but it probably is misleading.

13. 13 Lesson 5.5.1 Evaluating Claims Statistics aren’t always used in deliberately misleading ways. Sometimes, whether a claim is supported by data can be unclear for different reasons.

14. 14 Example 4 Solution follows… Lesson 5.5.1 Evaluating Claims At the swim meet, the team swam in three relay races. The times for each team member in each race are shown below. Lucas claims that he’s the fastest swimmer in the relay swim team. His sister, Sam, claims that Lucas is not the fastest. Whose claim do the results support? Solution It’s hard to tell just by looking at these results if Lucas is the fastest. He swam fastest in Race 1 and Race 3, but not in Race 2. One way to analyze the results is to find each person’s mean time. Lucas: (22.5 + 25.7 + 19.5) ÷ 3 = 22.6 s Latoya: (23.0 + 19.7 + 22.1) ÷ 3 = 21.6 s Jorge: (27.5 + 26.2 + 27.4) ÷ 3 = 27.0 s Anna: (23.1 + 20.2 + 21.4) ÷ 3 = 21.6 s Solution continues…

15. 15 Example 4 Lesson 5.5.1 Evaluating Claims At the swim meet, the team swam in three relay races. The times for each team member in each race are shown below. Lucas claims that he’s the fastest swimmer in the relay swim team. His sister, Sam, claims that Lucas is not the fastest. Whose claim do the results support? Solution (continued) Both Latoya and Anna had faster average times than Lucas. So Sam could say that the results support her claim. On the other hand, no one swam faster than Lucas’s time of 19.5 s. So Lucas could say that the results support his claim.

16. 16 Lesson 5.5.1 Evaluating Claims In cases like this, it’s not clear whose claim the data supports. Or you could look more closely at the data. Did something happen to Lucas in the second race to slow him down? Or perhaps he was doing a different stroke — maybe Lucas is fastest at one stroke, but not at another. The best thing is probably to say whether you’re interested in the fastest average time, or the fastest single time.

17. 17 Guided Practice Solution follows… Lesson 5.5.1 Evaluating Claims A babysitting company has six sitters of ages 13, 13, 14, 15, 15, and 45. Use this information for Exercises 4–7. 7. Make two claims that better represent the typical babysitter’s age. 6. The claim in Exercise 5 is valid, but why is it misleading? 5. The company claims that the typical age of its babysitters is 19. Which measure of central tendency supports this claim? 4. Find the mean, median, mode, and range of the babysitters’ ages. mean = 19.2 years; median = 14.5; modes = 13 and 15; range = 32 mean The mean is pulled upward by the much larger age of 45. All but one of its sitters are below 19. Typical age is 13–15. Most babysitters are under 20.

18. 18 Evaluating Claims Independent Practice Solution follows… Lesson 5.5.1 Use the terms data, valid, invalid, or claim to complete the sentences in Exercises 1–3. 4. Someone reading the circle graph on the right made this claim: "Most people on the school board are aged 40–49." Explain why this claim is invalid. Suggest why the person may have thought that this claim was true. 1. A __________ is a statement that is presented as a fact. 2. A claim is considered ______ if the _____ is incorrectly interpreted. 3. A claim is usually _________ if there is no ________ to support it. Less than half the people are aged 40-49. She may have thought this a valid claim because 40-49 is the group with most people in it. claim invaliddata invalid

19. 19 Evaluating Claims Independent Practice Solution follows… Lesson 5.5.1 Here are the ages of the counselors at a summer camp: {19, 20, 22, 23, 20, 55, 20} 5. Find the mode, median, and mean for this data set. 6. Most counselors are aged 24. Use your statistics from Exercise 5 to say whether the claims in Exercises 6–10 are valid or invalid. For each valid claim, say which statistic supports the claim. Are any of these claims valid but misleading? Explain your answer. 10. More than 14% of the counselors are over 30. 9. Half the counselors are 20 or younger. 8. Half the counselors are older than 24. 7. The typical age of the counselors is over 25. mean = 25.6; median = 20; mode = 20 Invalid Valid, though only supported by the mean, so possibly misleading. Valid, supported by the median. Valid, though possibly misleading, since only 1 person is over 30.

20. 20 Evaluating Claims Lesson 5.5.1 Round Up People often make claims. Either way, the claim won’t be valid. But sometimes the data doesn’t support the claims or has been misinterpreted. Often their claims are valid and backed up by data.