Consider a football team for whom the numbers on the active players’ jerseys are 29, 41, 50, 58, 79,…, 10
(listed in alphabetical order of the players’ names). Does it make sense to calculate the mean of those
numbers? Why or why not?
2. The Fair Isaac Corporation (FICO) credit rating scores obtained in a simple random sample are listed below:
714-751-664-789-818-779-698-836-753-834-693-802
a. Find mean, median, mode, and midrange.
b. As of this writing, the reported mean FICO score was 678. Do these sample FICO scores appear to be
consistent with the reported mean?
3. A student earned grades of 92, 83, 77, 84, and 82 on her five regular tests. She earned grades of 88 on the
final exam and 95 on her class projects. Her combined homework grade was 77. The five regular tests count
for 60% of the final grade, the final exam counts for 10%, the project counts for 15%, and homework counts
for 15%. What is her weighted mean grade?
4. Bao Xishun is the world’s tallest man with a height of 92.95 in. (or 7 ft. 8.95 in.). Men have heights with a
mean of 69.6 in. and a standard deviation of 2.8 in.
a. Convert Bao’s height to a z-score.
b. Does Bao’s height meet the criterion of being unusual by corresponding to a z-score that does not fall
between -2 and 2?
#1. Makes no sense to average jersey numbers
#2.
Order the scores to get
664 693 698 714 751 753 779 789 802 818 834 836
mean: 760.9
median: 752
mode: all are modes
midrange: 750
don't look consistent to me
#3.
.60(92+83+77+84+82)/5 + .10*88 + .15*95 + .15*77 = 84.76
#4.
(92.95-69.6)/2.8 = 8.34 std above the mean
1. For the football team, it does make sense to calculate the mean of the numbers on the jerseys. The mean is a measure of central tendency that summarizes the average value of a set of numbers. In this case, calculating the mean would give us the average jersey number of the active players. However, it is important to note that the given list of numbers is not complete, as it only goes up to 10. Therefore, it would not be possible to calculate the accurate mean with the given information.
2. a. To find the mean, we add up all the FICO scores and divide them by the number of scores:
Mean = (714 + 751 + 664 + 789 + 818 + 779 + 698 + 836 + 753 + 834 + 693 + 802) / 12
To find the median, we arrange the scores in ascending order and find the middle value:
(664, 693, 698, 714, 751, 753, 779, 789, 802, 818, 834, 836)
Median = (751 + 753) / 2
To find the mode, we identify the score that appears most frequently:
No score appears more than once, so there is no mode.
To find the midrange, we determine the average of the largest and smallest scores:
Midrange = (664 + 836) / 2
b. To determine if the sample FICO scores are consistent with the reported mean of 678, we can compare the calculated mean with the reported mean. If they are close, the scores appear to be consistent. If they are significantly different, then the sample FICO scores may not be representative of the population.
3. To calculate the weighted mean grade, we multiply each grade by its corresponding weight and then sum them up.
Weighted mean = (92 * 0.60) + (83 * 0.60) + (77 * 0.60) + (84 * 0.60) + (82 * 0.60) + (88 * 0.10) + (95 * 0.15) + (77 * 0.15)
4. a. To convert Bao's height to a z-score, we use the formula:
z-score = (x - mean) / standard deviation
In this case:
x = 92.95 inches (Bao's height)
mean = 69.6 inches (mean height for men)
standard deviation = 2.8 inches
z-score = (92.95 - 69.6) / 2.8
b. A z-score indicates how many standard deviations a data point is from the mean. In this case, we need to compare Bao's z-score to the range of -2 to 2, where values within this range are considered typical or not unusual. If Bao's z-score falls outside this range, his height would be considered unusual.