1. Histograms and Distributions

2. We have used dot plots to visualize small sets of data.
For larger sets of data a different type of graph will be more efficient.

3. The horizontal scale is quantitative and measures the data values.
A frequency distribution is a table that shows ranges of values and their frequency.
A frequency histogram is a type of bar graph that represents the frequencies of a data set.
The horizontal scale is quantitative and measures the data values.
The vertical scale measures the frequencies of the classes.
Consecutive bars must touch at class boundaries.
data
frequency

4. The following sample data set lists the prices (in dollars) of 30 portable global positioning system (GPS) navigators.
Fill in the frequency distribution for the data.
Construct a histogram of the data.

5. The Shape of Distributions
(negatively skewed)
(positively skewed)

6. Two hundred runners completed the annual Color Me Rad 5K race
Two hundred runners completed the annual Color Me Rad 5K race. The table displays the race times for the 200 runners.
Construct a histogram of the data.
Describe its shape.

7. The percentile rank of a value is the percentage of data that is below the given value.
Percentile ranks are used when there are many individual scores/data and is useful to compare individual performance.
Example: You are the fourth tallest person in a group of 20. What is your percentile rank? Interpret your percentile rank.

8. The percentile rank of a value is the percentage of data that is below the given value.
Example: You are the tallest person in a group of 20. What is your percentile rank? Interpret your percentile rank.

9. SAT Scores
Your percentile score tells you how you did on the SAT compared to everyone else who took it. If you got a percentile of 47 on the Math section, you did better than 47 percent of students on that particular section.
The percentile score is not like a grade out of 100. For example, if you get a percentile of 90, that doesn't mean you got exactly 90 percent of the questions right. It just means, compared to everyone who took the SAT, you scored higher than 90 percent of them. (the number of correct answers is reported as your “raw score.”)

10. SAT Composite Score Range
SAT Scores
SAT Composite Score Range
Percentile Score
99+
98 to 99
97 to 98
94 to 97
91 to 94
86 to 91
80 to 86
72 to 80
64 to 72
55 to 64
44 to 55
34 to 44
25 to 34
18 to 25
12 to 18
7 to 12
4 to 7
2 to 4
1 to 2 1
Something to note about these percentile ranks: they change the fastest with the middle scores. For example, the difference between a 1450 and a 1600 – the highest possible score – is only 3 percentile points, 97th to 99th.
However, the same point gap between 1100 and 1250 has a vast percentile difference – 55th to 80th. This means that if you have scored 1100 or lower, increasing your overall composite by just 150 points will have a vast boost to your percentile rank and your admissions competitiveness.