Batting Averages

1. What is the overall shape of the of the histogram, roughly symmetric or clearly skewed?

2. What is the approximate median of the batting averages?

3. What is the range if we ignore the outlier?

(a) Do a stemplot and describe its main features.

(b) Give the mean, variance(square of stdevn), and standard deviation.

Mean: , variance: , std deviation:

(c) Compute the median, quartiles, and IQR. Are there any outliers by the 1.5*IQR criterion?

Median: , quartiles: , IQR: , any outliers (yes, or no)?

(d) Based on the shape of the distribution, would you report the standard deviation or the quartiles as a measure of spread?

(a) Choose four numbers that have the lowest possible standard deviation.

(b) Choose four numbers that have the largest possible standard deviation.

(c) Is more than one choice possible in either a or b? Explain.

Use Table 1.3 data of percent of state residents at least age 65. Do a graphical display and give an appropriate numerical summary of the distribution. Justify your choice of measures.

Compute the Z-Scores for each player and give them below

Cobb

Williams

Brett

Which player was most above their peers?

(a)P(X > 700) =

(b) P(X < 500) =

(c) P(500< X <800) =

(a) What percent of pregnancies last less than 240 days?

(b) What percent of pregnancies last between 240 and 270 days?

(c) How long to the longest 20% of pregnancies last?

(a) What are the lower and upper deciles of the standard normal distribution?

(b) The length of human pregnancies is approximately normal with mean 266 days and standard deviation 16 days. What are the lower and upper deciles of this distribution?