Statistical Claims Unit 9 Lesson 13

Questions to Ask When Looking at Data and/or Graphs Is the information presented correctly? Is the graph trying to influence you? Does the scale use a regular interval? What impression is the graph giving you?

Why is this graph misleading? This title tells the reader what to think (that there are huge increases in price). The actual increase in price is 2,000 pounds, which is less than a 3% increase. The graph shows the second bar as being 3 times the size of the first bar, which implies a 300% increase in price. The scale moves from 0 to 80,000 in the same amount of space as 80,000 to 81,000.

A more accurate graph: An unbiased title A scale with a regular interval. This shows a more accurate picture of the increase.

Why is this graph misleading? The scale does not have a regular interval.

Graphs can be misleading in the news. The margin of error is the amount (usually in percentage points) that the results can be “ off by. ” Be wary of data with large margins of error.

From CNN.com

Problems: The difference in percentage points between Democrats and Republicans (and between Democrats and Independents) is 8% (62 – 54). Since the margin of error is 7%, it is likely that there is even less of a difference. The graph implies that the Democrats were 8 times more likely to agree with the decision. In truth, they were only slightly more likely to agree with the decision. The graph does not accurately demonstrate that a majority of all groups interviewed agreed with the decision.

CNN.com updates the graph:

What does the top of this graph show? About 12 million people are downloading music legally. Just over 9 million people are downloading music illegally. The bottom of the graph is misleading. Why? The graph implies that 1% of the iPods are filled with legally downloaded music. It implies that the other 99% are filled with illegally downloaded music. Why is this wrong?

What could be in those iPods besides legally downloaded music? Empty space – most people don ’ t have iPods that are filled to capacity. Songs that were added from legally purchased CDs. Games, calendars, other applications. Songs that were downloaded illegally. It is possible that the rest of the iPod contains some illegally downloaded music, but it is unlikely that 99% of a person’s iPod is filled with illegal music.

Starting Point Mayor Marcus is running for a second term against a challenger. Which graph should he send to the local journalist who is reporting on crime rates?

Example 1. Miss Flores asked some of her 6th grade math students how many hours of television they watch daily. Use the data in the table to calculate mean, median, and mode. These calculations will let us know how many hours are most typical per person. Hours of Television Viewed (Daily) NameTotal No. of Hours Sam1 Dominik2 Brianna1 Paul1 Mario3 Erica1 Maria2

Mean: = 11 = Median: Mode: The number 1 appears the most times. 1 is the mode. According to our calculations, most participants watch approximately 1 hour of television every day. ***Note: Even though we have a mean of 1.6, no participant watched exactly 1 and six-tenths of an hour of TV. This is an example of how a mean can describe the group but not any individual member of the group.

Mean: = 20 = Median: Median = 1.5 Mode: The number 1 appears the most times. 1 is the mode. According to our calculations, most participants watch between 1 and 2.5 of television every day. Did our mean change when we added Hannah’s information? How about the median? The mode? Would the median or mode change if Hannah watched 4 hours daily? 12 hours?

Example 3. Throughout most of the year, Acapulco is very sunny. If you look at the # of wet days from February through May, you see the range is from 0 to 2. But when the rainy season begins in June, the number of wet days jumps to is an outlier in this set of data because it is very different from the rest of the numbers. Number of wet days in Acapulco, Mexico February1 March0 April0 May2 June12

Feb - MayFeb - June Mean = 3 3 ÷ 4 = 0.75 Mean = = ÷ 5 = 3 Mean = 3 Median Median = Median = 1 Mode Mode = Mode = 0 The outlier did not affect the mode, and it changed the median slightly. But look what happens to the mean when the June number is included in the data. The mean becomes 3 wet days, which is the same as Feb through May combined.

With OutlierWithout Outlier Mean = ÷ 6 = 400 Mean = = ÷ 5 = 200 Mean = 200 Median Median = 200Median = 190 Mode Mode = 190 Identify the outlier. Then find the mean, median, and mode of the data with and without the outlier

Homework Time Page #1-14