Reading 2: organizing, visualizing, and describing data

Question 1

To perform meaningful mathematical analysis, an analyst must use data that are:
discrete.
numerical.
continuous.

Answer 1

We can perform mathematical operations on numerical data but not on categorical data. Numerical data can be discrete or continuous. (LOS 2.a)

Question 2

Which of the following types of data would most likely be organized as a two-dimensional array?
Panel.
Time series.
Cross sectional.

Answer 2

Panel data combine time series data with cross-sectional data and are typically organized as data tables, which are two-dimensional arrays. (LOS 2.a,b)

Question 3

The intervals in a frequency distribution should always be:
truncated.
open-ended.
non-overlapping.

Answer 3

ntervals within a frequency distribution should always be non-overlapping and closed-ended so that each data value can be placed into only one interval. Interval widths should be defined so that data are adequately summarized without losing valuable characteristics. (LOS 2.c)

Question 4

Consider the following contingency table from a political opinion poll:

In this table, the value 34% represents:

a joint frequency.
a marginal frequency.
an absolute frequency.

Answer 4

The value 34% is the joint probability that a voter supports both Jones and Williams. Because it is stated as a percentage, this value is a relative frequency. The totals for each row and column are marginal frequencies. An absolute frequency is a number of occurrences, not a percentage of occurrences. (LOS 2.d)

Question 5

The vertical axis of a histogram shows:
the frequency with which observations occur.
the range of observations within each interval.
the intervals into which the observations are arranged.

Answer 5

In a histogram, the intervals are on the horizontal axis and the frequency is on the vertical axis. (LOS 2.e)

Question 6

In which type of bar chart does the height or length of a bar represent the cumulative frequency for its category?
Stacked bar chart.
Grouped bar chart.
Clustered bar chart.

Answer 6

In a stacked bar chart, the height or length of a bar represents the cumulative frequency of a category. In a grouped or clustered bar chart, each category is displayed with bars side by side that together represent the cumulative frequency. (LOS 2.e)

Question 7

An analyst who wants to illustrate the relationships among three variables should most appropriately construct:
a bubble line chart.
a scatter plot matrix.
a frequency polygon.

Answer 7

With a scatter plot matrix, an analyst can visualize the relationships among three variables by organizing scatter plots of the relationships between each pair of variables. Bubble line charts are typically used to visualize two variables over time. Frequency polygons are best used to visualize distributions. (LOS 2.f)

Question 8

What is the arithmetic mean return for XYZ stock?

7.3%.
8.0%.
11.0%.

Chart: 2015:22%, 2016:5%, 2017:-7%, 2018:11%, 2019:2%, 2020:11%

Answer 8

[22% + 5% + –7% + 11% + 2% +11%] / 6 = 7.3% (LOS 2.g)

Question 9

What is the median return for XYZ stock?

7.3%.
8.0%.
11.0%.

Chart: 2015:22%, 2016:5%, 2017:-7%, 2018:11%, 2019:2%, 2020:11%

Answer 9

To find the median, rank the returns in order and take the middle value: –7%, 2%, 5%, 11%, 11%, 22%. In this case, because there is an even number of observations, the median is the average of the two middle values, or (5% + 11%) / 2 = 8.0%. (LOS 2.g)

Question 10

A data set has 100 observations. Which of the following measures of central tendency will be calculated using a denominator of 100?
The winsorized mean, but not the trimmed mean.
Both the trimmed mean and the winsorized mean.
Neither the trimmed mean nor the winsorized mean.

Answer 10

The winsorized mean substitutes a value for some of the largest and smallest observations. The trimmed mean removes some of the largest and smallest observations. (LOS 2.g)

Question 11

The harmonic mean of 3, 4, and 5 is:
3.74.
3.83.
4.12.

Answer 11

3.83

Question 12

The mean annual return on XYZ stock is most appropriately calculated using:

the harmonic mean.
the arithmetic mean.
the geometric mean.

Answer 12

Because returns are compounded, the geometric mean is appropriate.

Question 13

Given the following observations:
2, 4, 5, 6, 7, 9, 10, 11

The 65th percentile is closest to:

5.85.
6.55.
8.70.

Answer 13

With eight observations, the location of the 65th percentile is:

(8+1) x 65/100

The fifth observation is 7 and the sixth observation is 9, so the value at 5.85 observations is 7 + 0.85(9 – 7) = 8.7. (LOS 2.i)

Question 14

What is the sample standard deviation?

9.8%.
72.4%.
96.3%.

Chart: 2015:22%, 2016:5%, 2017:-7%, 2018:11%, 2019:2%, 2020:11%

Answer 14

sq 96.3

Question 15

Assume an investor has a target return of 11% for XYZ stock. What is the stock’s target downside deviation?

9.4%.
12.1%.
14.8%.

Answer 15

Deviations from the target return:
22% – 11% = 11%

5% – 11% = –6%

–7% – 11% = –18%

11% – 11% = 0%

2% – 11% = –9%

11% – 11% = 0%

Target downside deviation = sq 88.2

Question 16

Which of the following is most accurate regarding a distribution of returns that has a mean greater than its median?
It is positively skewed.
It is a symmetric distribution.
It has positive excess kurtosis.

Answer 16

A distribution with a mean greater than its median is positively skewed, or skewed to the right. The skew pulls the mean. Kurtosis deals with the overall shape of a distribution, not its skewness. (LOS 2.l)

Question 17

A distribution of returns that has a greater percentage of small deviations from the mean and a greater percentage of extremely large deviations from the mean compared with a normal distribution:
is positively skewed.
has positive excess kurtosis.
has negative excess kurtosis.

Answer 17

A distribution that has a greater percentage of small deviations from the mean and a greater percentage of extremely large deviations from the mean will be leptokurtic and will exhibit excess kurtosis (positive). The distribution will be more peaked and have fatter tails than a normal distribution. (LOS 2.m)

Question 18

The correlation between two variables is +0.25. The most appropriate way to interpret this value is to say:
a scatter plot of the two variables is likely to show a strong linear relationship.
when one variable is above its mean, the other variable tends to be above its mean as well.
a change in one of the variables usually causes the other variable to change in the same direction.

Answer 18

Correlation of +0.25 indicates a positive linear relationship between the variables—one tends to be above its mean when the other is above its mean. The value 0.25 indicates that the linear relationship is not particularly strong. Correlation does not imply causation. (LOS 2.n)