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Answer: A mutual fund is a professionally managed
Chapter 1, Problem 53E(choose chapter or problem)
A mutual fund is a professionally managed investment scheme that pools money from many investors and invests in a variety of securities. Growth funds focus primarily on increasing the value of investments, whereas blended funds seek a balance between current income and growth. Here is data on the expense ratio (expenses as a % of assets, from www.morningstar.com) for samples of 20 large-cap balanced funds and 20 large-cap growth funds (“large-cap” refers to the sizes of companies in which the funds invest; the population sizes are 825 and 762, respectively):
\(\begin{array}{cccccc} \text { Bl } & 1.03 & 1.23 & 1.10 & 1.64 & 1.30 \\ & 1.27 & 1.25 & 0.78 & 1.05 & 0.64 \\ & 0.94 & 2.86 & 1.05 & 0.75 & 0.09 \\ & 0.79 & 1.61 & 1.26 & 0.93 & 0.84 \\ & & & & & \\ \text { Gr } & 0.52 & 1.06 & 1.26 & 2.17 & 1.55 \\ & 0.99 & 1.10 & 1.07 & 1.81 & 2.05 \\ & 0.91 & 0.79 & 1.39 & 0.62 & 1.52 \\ & 1.02 & 1.10 & 1.78 & 1.01 & 1.15 \end{array}\)
a. Calculate and compare the values of \(\bar{x}\), \(\tilde{x}\) and s for the two types of funds.
b. Construct a comparative boxplot for the two types of funds, and comment on interesting features.
Questions & Answers
QUESTION:
A mutual fund is a professionally managed investment scheme that pools money from many investors and invests in a variety of securities. Growth funds focus primarily on increasing the value of investments, whereas blended funds seek a balance between current income and growth. Here is data on the expense ratio (expenses as a % of assets, from www.morningstar.com) for samples of 20 large-cap balanced funds and 20 large-cap growth funds (“large-cap” refers to the sizes of companies in which the funds invest; the population sizes are 825 and 762, respectively):
\(\begin{array}{cccccc} \text { Bl } & 1.03 & 1.23 & 1.10 & 1.64 & 1.30 \\ & 1.27 & 1.25 & 0.78 & 1.05 & 0.64 \\ & 0.94 & 2.86 & 1.05 & 0.75 & 0.09 \\ & 0.79 & 1.61 & 1.26 & 0.93 & 0.84 \\ & & & & & \\ \text { Gr } & 0.52 & 1.06 & 1.26 & 2.17 & 1.55 \\ & 0.99 & 1.10 & 1.07 & 1.81 & 2.05 \\ & 0.91 & 0.79 & 1.39 & 0.62 & 1.52 \\ & 1.02 & 1.10 & 1.78 & 1.01 & 1.15 \end{array}\)
a. Calculate and compare the values of \(\bar{x}\), \(\tilde{x}\) and s for the two types of funds.
b. Construct a comparative boxplot for the two types of funds, and comment on interesting features.
ANSWER:Step 1 of 4
(a):
We will calculate each value and compare the two types of funds.
1.
The sample mean \(\bar{x}\) of observations \(x_1,\ x_2,\ldots,x_n\) is given by
\(\bar{x}=\frac{x_{1}+x_{2}+\ldots+x_{n}}{n}=\frac{1}{n} \sum_{i=1}^{n} x_{i}\)
For the balanced fund data, we have
\(\begin{array}{l} \sum_{i=1}^{20} x_{i}=1.03+1.23+\ldots+0.84=22.41 \\ \bar{x}=\frac{1}{20} \cdot 22.41=1.121 \end{array}\)
For the growth fund data, we have
\(\begin{array}{l} \sum_{i=1}^{20} x_{i}=052+099+\ldots+1.15=24.87 \\ \bar{x}=\frac{1}{20} \cdot 24.87=1.244 \end{array}\)
We have that the sample mean is fairly bigger for the growth funds data.