Question

53. A mutual fund is a professionally managed invest- ment scheme that pools money from many investors and invests in a variety of securities. Growth funds focus primarily on increasing the value of invest- ments, 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 bal- anced 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): BI 103 1.23 110 1.64 1.30 1.27 1.25 0.78 .05 0.64 0.94 2.86 1.05 0.75 0.09 0.79 1.6 26 0.93 0.84 Gr 0.52 1.06 1.26 2.17 1.55 0.99 1.10 1.07 181 2.05 0.91 0.79 1.39 0.62 1.52 1.02 1.10 1.78 .0 1.15 Calculate and compare the values of x, x , and s for the two types of funds Construct a comparative boxplot for the two types of a. b. funds, and comment on interesting features.

Answer 1

a.

$\begin{matrix} Variable & Mean(\bar{x})& StDev(s)& Median(\tilde{x})\\ B1 & 1.121 & 0.536 & 1.050\\ Gr & 1.244 & 0.448 & 1.100 \end{matrix}$

b.

From box plots, we observe that distribution of Fund B1 is symmetric whereas the distribution of fund Gr is positively skewed and the Fund B1 is less scattered than Fund Gr. However in Fund B1 there exists two outliers i.e. 0.09 and 2.86. Lastly median of Fund B1> median of Fund Gr.