A magazine's list of the world's most admired companies for 2014 is provided in the data below. The data in the column labeled "Return" shows the one-year total return (%) for the top ranked 50 companies. For the same time period the S&P average return was 18.4%. Rank Company Name Return (%) 1 Company A 14.8 2 Company B 28.8 3 Company C 48.3 4 Company D 12.7 5 Company E 27.1 6 Company F 1.4 7 Company G 32.8 8 Company H 23.4 9 Company I 85.5 10 Company J 12.3 11 Company K 39.6 12 Company L 9.1 13 Company M 31.8 14 Company N 14.1 15 Company O 5.1 16 Company P −11.4 17 Company Q 5.8 18 Company R −12.9 19 Company S 20.5 20 Company T 14 21 Company U −13.9 22 Company V 0.8 23 Company W 29.3 24 Company X 35.2 25 Company Y 32.3 Rank Company Name Return (%) 26 Company Z 64.2 27 Company AA 3.5 28 Company BB 5.5 29 Company CC −8.6 30 Company DD 16.3 31 Company EE 4.7 32 Company FF 18.3 33 Company GG −3 34 Company HH 9 35 Company II 31.6 36 Company JJ 7.1 37 Company KK −7.3 38 Company LL 116.1 39 Company MM 21.7 40 Company NN 16.7 41 Company OO 25.2 42 Company PP 12.7 43 Company QQ 35.3 44 Company RR −5.1 45 Company SS 7.3 46 Company TT −6.1 47 Company UU 15.3 48 Company VV 115.6 49 Company WW 6.4 50 Company XX −3.5 (a) Compute the median return (in %) for the top-ranked 50 companies. % (b) What percentage of the top-ranked 50 companies had a one-year return greater than the S&P average return? % (c) Develop the five-number summary (in %) for the data. minimum % first quartile % median % third quartile % maximum %
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A magazine's list of the world's most admired companies for 2014 is provided in the data below. The data in the column labeled "Return" shows the one-year total return (%) for the top ranked 50 companies. For the same time period the S&P average return was 18.4%.
Rank Company
Name Return
(%)
1 Company A 14.8
2 Company B 28.8
3 Company C 48.3
4 Company D 12.7
5 Company E 27.1
6 Company F 1.4
7 Company G 32.8
8 Company H 23.4
9 Company I 85.5
10 Company J 12.3
11 Company K 39.6
12 Company L 9.1
13 Company M 31.8
14 Company N 14.1
15 Company O 5.1
16 Company P −11.4
17 Company Q 5.8
18 Company R −12.9
19 Company S 20.5
20 Company T 14
21 Company U −13.9
22 Company V 0.8
23 Company W 29.3
24 Company X 35.2
25 Company Y 32.3
Rank Company
Name Return
(%)
26 Company Z 64.2
27 Company AA 3.5
28 Company BB 5.5
29 Company CC −8.6
30 Company DD 16.3
31 Company EE 4.7
32 Company FF 18.3
33 Company GG −3
34 Company HH 9
35 Company II 31.6
36 Company JJ 7.1
37 Company KK −7.3
38 Company LL 116.1
39 Company MM 21.7
40 Company NN 16.7
41 Company OO 25.2
42 Company PP 12.7
43 Company QQ 35.3
44 Company RR −5.1
45 Company SS 7.3
46 Company TT −6.1
47 Company UU 15.3
48 Company VV 115.6
49 Company WW 6.4
50 Company XX −3.5
(a)
Compute the
%
(b)
What percentage of the top-ranked 50 companies had a one-year return greater than the S&P average return?
%
(c)
Develop the five-number summary (in %) for the data.
minimum
%
first
%
median
%
third quartile
%
maximum
%
(d)
Compute the lower and upper limits (in %).
lower limit
.
%
upper limit
%
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