Inverse SATs Critical reading SAT scores are distributed as N 500 , 100 . a. Find the SAT score at the 75th percentile. b. Find the SAT score at the 25th percentile. c. Find the interquartile range for SAT scores. d. Is the interquartile range larger or smaller than the standard deviation? Explain.
Inverse SATs Critical reading SAT scores are distributed as N 500 , 100 . a. Find the SAT score at the 75th percentile. b. Find the SAT score at the 25th percentile. c. Find the interquartile range for SAT scores. d. Is the interquartile range larger or smaller than the standard deviation? Explain.
Solution Summary: The author explains how to determine the SAT score at the 75th percentile.
Inverse SATs Critical reading SAT scores are distributed as
N
500
,
100
.
a. Find the SAT score at the 75th percentile.
b. Find the SAT score at the 25th percentile.
c. Find the interquartile range for SAT scores.
d. Is the interquartile range larger or smaller than the standard deviation? Explain.
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
The average number of minutes Americans commute to work is 27.7 minutes (Sterling's Best Places, April 13, 2012). The average commute time in minutes for 48 cities are as follows:
Click on the datafile logo to reference the data.
DATA file
Albuquerque
23.3
Jacksonville
26.2
Phoenix
28.3
Atlanta
28.3
Kansas City
23.4
Pittsburgh
25.0
Austin
24.6
Las Vegas
28.4
Portland
26.4
Baltimore
32.1
Little Rock
20.1
Providence
23.6
Boston
31.7
Los Angeles
32.2
Richmond
23.4
Charlotte
25.8
Louisville
21.4
Sacramento
25.8
Chicago
38.1
Memphis
23.8
Salt Lake City
20.2
Cincinnati
24.9
Miami
30.7
San Antonio
26.1
Cleveland
26.8
Milwaukee
24.8
San Diego
24.8
Columbus
23.4
Minneapolis
23.6
San Francisco
32.6
Dallas
28.5
Nashville
25.3
San Jose
28.5
Denver
28.1
New Orleans
31.7
Seattle
27.3
Detroit
29.3
New York
43.8
St. Louis
26.8
El Paso
24.4
Oklahoma City
22.0
Tucson
24.0
Fresno
23.0
Orlando
27.1
Tulsa
20.1
Indianapolis
24.8
Philadelphia
34.2
Washington, D.C.
32.8
a. What is the mean commute time for…
Morningstar tracks the total return for a large number of mutual funds. The following table shows the total return and the number of funds for four categories of mutual funds.
Click on the datafile logo to reference the data.
DATA file
Type of Fund
Domestic Equity
Number of Funds
Total Return (%)
9191
4.65
International Equity
2621
18.15
Hybrid
1419
2900
11.36
6.75
Specialty Stock
a. Using the number of funds as weights, compute the weighted average total return for these mutual funds. (to 2 decimals)
%
b. Is there any difficulty associated with using the "number of funds" as the weights in computing the weighted average total return in part (a)? Discuss. What else might be used for weights?
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c. Suppose you invested $10,000 in this group of mutual funds and diversified the investment by placing $2000 in Domestic Equity funds, $4000 in International Equity funds, $3000 in Specialty Stock…
The days to maturity for a sample of five money market funds are shown here. The dollar amounts invested in the funds are provided.
Days to
Maturity
20
Dollar Value
($ millions)
20
12
30
7
10
5
6
15
10
Use the weighted mean to determine the mean number of days to maturity for dollars invested in these five money market funds (to 1 decimal).
days
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