Descriptive Stats
Sharpe ratio
(return-Riskfree)/standard deviation
Which measure of central tendency can be used for both numerical and categorical variables?
Mode
A summary measure of a characteristic of an entire population is called a:
Parameter
Data in a frequency distribution must
belong to only one group or interval. Intervals are mutually exclusive and non-overlapping.
The correlation coefficient is calculated by
dividing the covariance of two random variables by the product of their standard deviations.
Which one of the following alternatives best describes the primary use of inferential statistics? Inferential statistics are used to:
make forecasts, estimates or judgments about a large set of data based on statistical characteristics of a smaller sample.
A distribution with a mode of 10 and a range of 2 to 25 would most likely be:
skewed to the right/ positively skewed -The distance to the left from the mode to the beginning of the range is 8. The distance to the right from the mode to the end of the range is 15. Therefore, the distribution is skewed to the right, which means that it is positively skewed.
A summary measure that is computed to describe a population characteristic from a sample is called a
statistic
Variance equals the
sum of the squared deviations from the mean times the probability that that each outcome will occur.
For estimating a compound return over more than one year
the geometric mean of the historical returns is the most appropriate estimator.
Ratio Scale
Ratio scales are the strongest level of measurement; they quantify differences in the size of data and have a true zero point as the origin.
Ordinal Scale
The ordinal scale of measurement categorizes and orders data with respect to some characteristic
A higher Sharpe ratio indicates:
a higher excess return per unit of risk.
A distribution with a mean that is less than its median is
a negatively skewed distribution
A parameter is
any descriptive measure of a population characteristic.
A frequency distribution is a grouping of:
data into intervals (classes) so that the number of observations in each of the non-overlapping intervals (classes) can be seen and tallied.
A distribution that has a greater percentage of small deviations from the mean and a greater percentage of large deviations from the mean will be
leptokurtic and will exhibit positive excess kurtosis. The distribution will be taller (more peaked) with fatter tails than a normal distribution.
A negatively skewed distribution is characterized by
many small gains and a few extreme losses.
skewedness
measures the degree to which a distribution is not symmetric about its mean
Kurtosis
measures the peakedness of a distribution reflecting a greater or lesser concentration of returns around the mean. -is used to reflect the probability of extreme outcomes for a return distribution.
the median is equal to the ______ in a normal distribution
mode in a normal distribution the median is equal to the mode.
A leptokurtic distribution is
more peaked than normal and has fatter tails. and the excess kurtosis is greater than zero.
The arithmetic mean may be used to estimate the average return
over a one-period time horizon because it is the average of one-period returns.
Given a series of historical returns what is the best estimator of the next year's return.
the arithmetic mean is statistically the best estimator of the next year's return.
if a distribution is skewed
the magnitude of positive deviations from the mean is different from the magnitude of negative deviations from the mean.
investors are attracted to positive skewness because
the mean return is greater than the median return.
If the distribution is skewed to the left, then
the mean will be less than the median.
For a positively skewed distribution
the mode is less than the median, which is less than the mean (the mean is greatest).
When creating intervals around the mean to indicate the dispersion of outcomes, which of the following measures is the most useful?
the standard deviation
The coefficient of variation equals
the standard deviation divided by the mean.
The kurtosis for all normal distributions is
three
The difference between the geometric mean and the arithmetic mean increases
with an increase in variability between period-to-period observations.
The geometric mean calculates the rate of return that
would have to be earned each year to match the actual, cumulative investment performance.
Chebyshev's Inequality states that for any set of observations, the proportion of observations that lie within k standard deviations of the mean is at least
1-(1/k^2) We can use Chebyshev's Inequality to measure the minimum amount of dispersion whether the distribution is normal or skewed.
In a skewed distribution, what is the minimum proportion of observations between +/- two standard deviations from the mean?
75% 1-(1/k^2)
Frequency distribution
A frequency distribution is a tabular presentation of statistical data that aids the analysis of large data sets
Which of the following is an example of a parameter?
A parameter is any descriptive measure of a population characteristic. The population variance describes a population so it is a parameter. -the sample standard deviation and sample mean are each descriptive measures of samples.
Normal distribution +/- 1 standard deviation
Approximately 68% of the observations lie within +/- 1 standard deviation of the mean.
Descriptive statistics are used to:
Descriptive statistics are used mainly to summarize important characteristics of large data sets.
What is the main difference between descriptive statistics and inferential statistics?
Descriptive statistics are used to summarize a large data set while inferential statistics involves procedures used to make forecasts or judgments about a large data set by examining a smaller sample.
The relative frequency is the percentage of total observations falling within each interval.
It is found by taking the frequency of the interval and dividing that number by the sum of all frequencies.
Which measure of scale has a true zero point as the origin?
Ratio Scale