3. Describing Data Numerically

The following data represent the length of time (in minutes) between eruptions of Old Faithful in Yellowstone National Park.

a. Approximate the mean length of time between eruptions. .

The Federal Reserve Bank of St. Louis reported two average personal incomes for 2018: \$33,706 and \$50,731. One of these averages is the mean and the other is the median. Which is the mean? Support your answer.

Why is the median resistant, but the mean is not?

"Putting It Together: Lupus Based on historical birthing records, the proportion of males born worldwide is 0.51. In other words, the commonly held belief that boys are just as likely as girls is false. Systematic lupus erythematosus (SLE), or lupus for short, is a disease in which one’s immune system attacks healthy cells and tissue by mistake. It is well known that lupus tends to exist more in females than in males. Researchers wondered, however, if families with a child who had lupus had a lower ratio of males to females than the general population. If this were true, it would suggest that something happens during conception that causes males to be conceived at a lower rate when the SLE gene is present. To determine if this hypothesis is true, the researchers obtained records of families with a child who had SLE. A total of 23 males and 79 females were found to have SLE. The 23 males with SLE had a total of 23 male siblings and 22 female siblings. The 79 females with SLE had a total of 69 male siblings and 80 female siblings.

c. There are a total of 23+69=92 male siblings in the study. How many female siblings are in the study?

"Kiosks Yolanda opened a new fast food restaurant. From her first customer, Yolanda kept track of the time a patron needed to wait from the time placing the order to the time the customer received his/her order. Because she was unhappy with the wait time, she invested in Kiosks to take orders with the goal of decreasing wait times. In a random sample of 20 customers, it was found the wait time was 52.3 seconds.

b. Determine the mean wait time of the 10,303 customers."

"Birth Weights Suppose birth weights of babies are approximately normal with a mean of 3570 grams and a standard deviation of 495 grams. In a random sample of 15 mothers who were smokers during pregnancy, the mean birth weight of the babies was 3481.6 grams.

b. Simulate obtaining 2000 simple random samples for size n=15 babies from a population that is normally distributed with mean 3570 and standard deviation 495. For each sample, determine the sample mean. Draw a histogram of the 2000 sample means. Explain what each sample mean represents."

[NW] [DATA] TelevisionsIn the Sullivan Statistics Survey I, individuals were asked to disclose the number of televisions in their household. In the following probability distribution, the random variable X represents the number of televisions in households.

c. Calculate and explain the mean of the random variable X.