Question

5 from unit 1, lesson 14 here are some summary statistics about the number of accounts that follow some bands on social media. mean: 15,976 followers standard deviation: 3,279 followers q1: 13,796 median: 16,432 followers q3: 19,070 iqr: 5,274 followers a. give an example of a number of followers that a very popular band might have that would be considered an outlier for this data. explain or show your reasoning. b. give an example of a number of followers that a relatively unknown band might have that would be considered an outlier for this data. explain or show your reasoning. 6 from unit 1, lesson 13 the weights of one population of brown bears have a mean of 428 pounds and standard deviation of 36 pounds. the weights of another population of brown bears have a mean of 397 pounds and standard deviation of 25 pounds. andre says the two populations are similar. do you agree? explain your reasoning.

Explanation:

Step1: Recall outlier formula

Outliers are values outside $Q1 - 1.5\times IQR$ or $Q3+1.5\times IQR$.

Step2: Calculate upper - bound for non - outlier

$Q3 + 1.5\times IQR=19070+1.5\times5274$.
$19070 + 1.5\times5274=19070 + 7911=26981$.
So a very popular band's outlier would be greater than 26981, e.g., 30000.

Step3: Calculate lower - bound for non - outlier

$Q1-1.5\times IQR=13796 - 1.5\times5274$.
$13796-1.5\times5274=13796 - 7911 = 5885$.
So a relatively unknown band's outlier would be less than 5885, e.g., 3000.

Step4: Analyze brown bear populations

For comparing populations, large differences in means (428 vs 397) and different standard deviations (36 vs 25) mean they are not similar.

Answer:

a. 30000. Reason: Values greater than $Q3 + 1.5\times IQR=26981$ are outliers for popular bands.
b. 3000. Reason: Values less than $Q1-1.5\times IQR = 5885$ are outliers for unknown bands.
For question 6: No. Reason: Large differences in means and standard deviations.