http://www.ck12.org Chapter 1. An Introduction to Analyzing Statistical Data
b. mean 89. 23
c. median 89
d. upper and lower quartilesQ 1 = 87 ,Q 3 = 97. 5
e. midrange 80. 5
f. range37- The 62 is an outlier in the data set. This would usually cause the mean to be significantly lower than
the median, but the three 99’s are balancing this out. When we remove the 62, the mode should not be
affected. The mean should increase. The most dramatic changes will occur in the midrange and range.
The range should be much smaller and the midrange should increase. We would expect little change to
the medians and quartiles as they are resistant measures. - ̄x= 12. 99
2.s= 0. 264
3.s^2 = 0. 07 - The standard deviation tells you that the “typical” or “average” bag of chips in this sample is within
0 .07 grams of the mean weight. Based on our sample, we would not have reason to believe that the
company is selling unusually light or heavy bags of chips. Their quality control department appears to
be doing a good job! (Note: this answer is very subjective for now, but it is important to start thinking in
this manner. In later chapters, we will examine more precise measures and conclusions for this process.) - (a) Mode: 60 km^2 Mean: 439.3 km^2 Median: 42 km^2 Upper Quartile: 558 km^2 Lower Quartile: 4.9 km^2
Range: 2639.67 km^2 Standard Deviation: 1088.69 km^2 (b) There is oneveryextreme outlier. Isabela is by far
the largest island. In addition to that, there are many points in the lower half of the data that are very closely
grouped together. Many of these islands are volcanic rock that barely poke above the surface of the ocean. The
upper 50% of the data is much more spread out. This creates a situation in which the median stays very small,
but the mean will be strongly pulled towards the larger numbers because it is not resistant. (c) The standard
deviation is a statistic that is based on the mean. Therefore, if the mean is not resistant, the standard deviation
is not, and it will also be influenced by the larger numbers. If it is a measure of the “typical” distance from
the mean, then the larger points will have a disproportionate influence on the calculation. On a more intuitive
level, if the upper 50% of the data is very widely spread, the standard deviation reflects that extreme variation. - (a) Will vary (b) Will vary (c) Mean: the average salary of the players on this team in 2007. Median: the salary
at which half the players on the team make more than that, and half the players make less than that. Mode: the
salary that more players make than any other individual salary. Usually, this is a league minimum salary that
many players make. Midrange: The mean of just the highest paid and lowest paid players. Lower Quartile:
The salary at which only 25% of the players on the team make less. Upper Quartile: The salary at which 75%
of the players make less, or the salary at which only one quarter of the team makes more. IQR: The middle
50% of the players varies by this amount. (d) Range: The gap in salary between the highest- and lowest-paid
players. Standard Deviation: the amount by which a typical player’s salary varies from the mean salary. (e).
(f) Answers will vary, but students should comment on spread in one sentence and center in the other. Since
many baseball teams have a few star players who make much higher salaries, most examples should give the
students an opportunity to comment on the presence of outliers and their affect on the statistical measures of
center and spread.