Austin Hardy 720003930

Homework 3

1. Outliers in percent of older residentsa. Five number summary:

5.7, 11.7, 12.75, 13.5, 17.6

b. Does the 1.5 x IQR rule identify Alaska and Florida as suspected outliers? Does it flag any other states?

Q3 – Q1 = IQR

13.5 – 11.7 = 1.8 x 1.5 = 2.7 Outliers would lie below 9.0% and above 16.2%, therefore Alaska and Florida would both be outliers, along with one other unnamed state.

2. Mean versus median for oil wellsa. The mean of this data is: 48.24844.

The median of this data is: (37.7 +37.9)/2 = 37.8.The mean is significantly larger than the median because the values steadily increase until they reach the 90 to 100 range, where they increase much more rapidly, with an outlier of over 200. The histogram graph of this data would be skewed to the right in this case. This causes the mean to be greater, though the median would be unaffected.

3. How does the median change?

The mean is affected a significant amount because it is not a resistant measure (it increases from 81,875 dollars to 98,750 dollars), while the median value for the data would be unaffected, as the owner’s salary is the highest in both cases (35,000 dollars).

4. Hummingbirds and Flowers

Austin Hardy 720003930

5. Shakespeare’s Playsa. Median length of words used by Shakespeare: The median length would be

four words, as the percent of four letter words falls in the 50th percentile range (from about 46% to 71 %), and the graph is skewed to the right, allowing for a somewhat greater median.

b. Quartiles: The quartiles would be Q1 = 3, as the 25th percentile falls in the percentage of three letter words, and Q3 = 5, as the 75th percentile falls in the percentage of 5 letter words

c. Five Number Summary: The five number summary would be 1, 3, 4, 5, 12.

6. Create a Data Set

For the mean to equal 7, with 5 numbers, the total sum of the numbers must be 35. For the median to equal 10, the middle number must be 10, and there must be two numbers larger than 10, and two numbers smaller than 10. This gives me:

1, 2, 10, 11, 11