Statistics. Wednesday, March 28, 2012

Transcription

1 Statistics Wednesday, March 28, 2012 Today's Agenda: 1. Collect HW #2: Activities 9 7 & Go over HW #1: Activities 9 20 a f & Practice calculating & s x 4. Activities 9 4, 9 5, 9 11, Start HW #3: 9 8, 9 14, work on posters & finish revisions of your written report

2

3 Activity 9 4: Placement Exam Scores Frequency Placement Score (a) Does the distribution appear to be symmetric and mound shaped? (b) Consider how many scores fall within one standard deviation of the mean. (c) Refer back to the table of tallied scores to determine how many of the 213 scores fall within one standard deviation of the mean. What proportion of the 213 is this? (d) Determine how many of the 213 scores fall within two standard deviations of the mean. (Between and ) What proportion of the 213 is this? (e) Determine how many of the 213 scores fall within three standard deviations of the mean. (Between and ) What proportion of the 213 is this?

4 Vocabulary: Empirical Rule = Within a mound shaped, symmetric (normal) distribution 68% of the data falls within + or one standard deviation from the mean, 95% of the data falls within + or two standard deviations from the mean, 99.7% of the data falls within + or three standard deviations from the mean. Activity 9 5: SATs and ACTs SAT mean = 1500 ACT mean = 21 SAT standard deviation = 240 ACT standard deviation = 6 (a) If Bobby scored 1740 on the SAT, how many points above the SAT mean did he score? (b) If Kathy scored 30 on the ACT, how many points above the ACT mean did she score? (c) Is it sensible to conclude that because Bobby's difference is bigger that he outperformed Kathy on the admissions test? Explain. SAT mean = 1500 SAT standard deviation = 240 ACT mean = 21 ACT standard deviation = 6 (d) Determine how many standard deviations above the mean Bobby scored by dividing your answer to part a by the standard deviation of the SAT scores. (e) Determine how many standard deviations above the mean Kathy scored by dividing your answer to part (b) by the standard deviation of the ACT scores. Vocabulary: z score = an indication of how many standard deviations above or below the mean a given data point is calculated by (observation mean) standardization = the process of converting data from different scales to a common scale so a more accurate comparison can be made between them (f) Who had the higher z score on their admissions test? standard deviation (g) Who performed better on his or her admissions test compared to his or her peers?

5 SAT mean = 1500 ACT mean = 21 SAT standard deviation = 240 ACT standard deviation = 6 (h) Calculate the z score for Peter who scored 1380 on the SAT. Calculate the z score for Kelly who scored 15 on the ACT. (i) Does Peter or Kelly have the higher z score? (j) What does it mean to have a negative z score? Activity 9 11: Baby Weights a. 3 month old data: national average = 12.5 pounds national standard deviation = 1.5 pounds Benjamin = 13.9 pounds Determine the z score for Benjamin's weight at 3 months. Interpret what the z score means in context in a sentence. b. 6 month old data: national average = pounds national standard deviation = 2.0 pounds If Benjamin had the same z score at 6 months as he did at 3 months, determine how much a 6 month old Benjamin would weigh.

6 Activity 9 13: Baseball Lineups What will happen to measures of center and spread when we add a constant to each item in a list? a. If every player in the Yankee's lineup was two years older than reported, how would expect this change to affect the mean? How would you expect this change to affect the median? b. Calculate the new mean and median. Use may your calculator. mean = median = c. How would you expect this change to affect the range? How would you expect this change to affect the IQR? How would you expect this change to affect the standard deviation? d. Calculate the new range, IQR, and standard deviation. range = IQR = Adding or subtracting a constant to a list of numbers will move the mean and median up if adding or down if subtracting. The measures of center do not change. What will happen to measures of center and spread when we multiply each item in a list by a constant? e. If every player in the Tiger's lineup was double the age reported, how would expect this change to affect the mean? How would you expect this change to affect the median? f. Calculate the new mean and median. Use may your calculator. mean = median = g. How would you expect this change to affect the range? How would you expect this change to affect the IQR? How would you expect this change to affect the standard deviation? d. Calculate the new range, IQR, and standard deviation. range = IQR = Multiplying or dividing by a constant will change both the measures of center and spread. If you are multiplying, all measures of center and spread will be multiplied by that number. If you are dividing, all measures of center and spread will be divided by that number.

7 HW #3: Activities 9 8 & 9 14 use the data list from the Preliminaries and 9 12