Central Bucks School District



Stat and Data Analysis Name: _____________________

Activity 3.1A Date: _______________ Blk ____

1. Here are the class heights rounded to the nearest inch.

72 |69 |65 |66 |64 |66 |71 |66 |62 |73 |72 |68 |67 |71 | |70 |67 |62 |72 |67 |59 |74 |74 |68 |68 |64 |72 |72 |67 | |65 |64 |67 |65 |61 |67 |58 |72 |71 |66 |64 |70 |74 |67 | |62 |73 |73 |65 |62 |72 |74 |71 |66 |65 |64 |66 |65 |70 | |

2. Create a dotplot for the class data. Circle the dot that represents you.

[pic]

3. How many students have heights less than or equal to your height?

4. How many students have heights less than your height?

5. What percent of the class has height less than or equal to your height?

6. What percent of the class has height less than your height?

7. Both the previous percentages are possible definitions of percentiles of a distribution. Both give the percent of scores below a certain score. How different are the values?

8. From page 103 in the book: Copy the following…

a. Percentile Definition (In the blue box):

b. Alternate Definition (in bold in middle of p.103):

9. Calculate the following summary statistics from the class data:

Mean |St. Dev |n |Min |Q1 |Med |Q3 |Max | | | | | | | | | | |Using the book's definition of percentile, what percentile is the median of the class data?

10. Using the alternate definition of percentile, what percentile is the median of the class data?

11. The median is considered the 50th percentile. Why might the values you calculated in #10 & #11 not give you 50%?

13. Where does your height fall relative to the mean? Is it above or below the mean?

14. How far above or below? Take your height and subtract it by the mean height. [pic]

a. What is the difference of your height to the mean?

b. What is the difference of your partner's (person sitting next to you) height to the mean?

c. Would a positive difference mean your height is higher or lower than the mean height?

d. What would a negative difference mean?

15. How many standard deviations above or below the mean height is your height? Take your difference and divide it by the standard deviation. [pic] This number tells you how many standard deviations your height is from the mean height.

a. How many standard deviations above or below the mean height is your height?

b. How many standard deviations above or below the mean height is your partner's height?

16. This value is known as the standardized value of the height. It is also commonly called the z-score with this formula:[pic]

a. What is the shortest height? What z-score does this height have?

b. What is the tallest height? What z-score does this height have?

c. If your friend had a z-score of +1.30, what would this mean about his height? How tall would he be?

d. If another friend had a z-score of -2.10, what would this mean about her height? How tall would she be?

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