Chapter 3: Descriptive Measures

Identify each quantity as a parameter or a statistic:

a. \(\mu \)

b. \(s\)

c. \(\bar{x}\)

d. \(\sigma \)

Although, in practice, sample data are generally analyzed in inferential studies, what is ultimate objectives of such studies ?

Microwave Popcorn. For a given brand of microwave popcorn, what property is desirable for the population standard deviation of the cooking time? Explain your answer.

Fill in the following blanks.

(a) A standardized variable always has mean _____ and standard deviation _______ .

(b) The z-score corresponding to an observed value of a variable tells you ______ .

(c) A positive z-score indicates that the observation is ______ the mean, whereas a negative z-score indicates that the observation is _______ the mean.

Identify the statistic that is used to estimate

(a) A population mean.

(b) A population standard deviation.

Augusta National Golf Course. Earlier in this section, we found that the population mean length of the holes at the Augusta National Golf Club is $413.1yd$. In this context, is the number$413.1$a parameter or a statistic? Explain your answer.

Augusta National Golf Course. Earlier in this section, we found that the population standard deviation of the lengths of the holes at the Augusta National Golf Club is $132.0yd$. In this context. is the number $132.0$a parameter or a statistic? Explain your answer.

Heights of Basketball Players. In Section 3.2, we analyzed the heights of the starting five players on each of two men's college basketball teams. The heights, in inches, of the players on Team II are $67,72,76,76,and84.$Regarding the five players as a population. solve the following problems.

a. Compute the population mean height, $\mu$

b. Compute the population standard deviation of the heights,$\sigma$

Heights of Basketball Players. In Section $3.2$, we analyzed the heights of the starting five players on each of two men's college basketball teams. The heights, in inches, of the players on Team II are $67,72,76,76$and $84$. Regarding the five players as a population. solve the following problems.

a. Compute the population mean height, $\mu$.

b. Compute the population standard deviation of the heights, $\sigma$.

Name and describe the three most important measures of center.