Business Statistics - Ch. 4

Pat's time in the 1600 meter run placed Pat in the 85th percentile in the school. What percentage of students are faster than Pat?

15

The second quartile is also the:

50th percentile. median.

A unit-free measure of dispersion is

COEFFICIENT OF VARIATION

The numerical measure, σXY, is used frequently by financial portfolio managers. This measure is called the

COVARIANCE

Match the data characteristic to what it describes. Center, Variability, Shape

Center: typical or middle value; where the data values are concentrated Variability: spread of data values or dispersion Shape: symmetrical or skewed

Which of the following can be used to determine the proportion of data points that fall within a specified number of standard deviations from the mean?

Chebyshev's Theorem The empirical rule - assuming a normal distribution

True or false: Chebyshev's Theorem should only be applied to data sets that are normally distributed.

False

True or false: The standard deviation can be a negative value.

False

Which of the following situations are valid reasons for removing an outlier from a data set?

If the observed value was taken from a population different from the one under study. If the data point was typed incorrectly into the spreadsheet.

Which characteristic does NOT describe the range?

It considers all data values in the data set.

Which of the following is NOT a characteristic of the midrange?

It is robust to outliers.

Which shape matches the mean and median relationship?

Left skewed: mean < median Right skewed: mean > median Symmetrical: mean = median

The measure of center where half the values of the data set lie above this measure and half the values of the data set lie below this measure is known as the

Median

The measure of central location that can best be labeled as the midpoint of the data set is the

Median

Match the following terms with their meanings:

Mesokurtic: normal bell-shaped distribution Platykurtic: a flatter distribution than normal with heavier tails Leptokurtic: a sharply peaked distribution with thinners tails

The best measure of central location when using an attribute data set is the ___.

Mode

Which measure of center is the most frequently occurring value?

Mode

When estimating sigma using the following formula: xmax−xmin\6, one is assuming the distribution is

Normal

Find the first and third quartiles from the following data set using the method of medians: 2, 3, 3, 5, 6, 8, 12.

Q1 = 3, Q3 = 8

For the data set 4, 5, 6, and 9, the arithmetic mean is

Six

When comparing two data sets with different units of measurement, what is the relative measure of dispersion?

The coefficient of variation

A box plot is constructed using several different values. Which of the following values from a data set are included in a box plot?

The largest value The first quartile

A box plot is constructed using several different values. Which of the following values are included in a box plot

The second quartile The third quartile The smallest value

Which of the items below describes the usefulness of a standard deviation?

To gauge the relative position of data values within the data set.

True of false: When a data set is tabulated into bins, we lose information about the location of the x values within bins but gain clarity of presentation because grouped data can be displayed more compactly than raw data.

True

True or false: The arithmetic mean is the average of a data set.

True

True or false: The empirical rule should be applied to data sets that are normally distributed or nearly normally distributed.

True

Which of the following statements is true?

Two data sets could have the same mean but different standard deviations. Two data sets could have different means but the same standard deviation.

The average squared difference of data values from their mean is the

Variance.

The mean is the balancing point because it has the property that distances from the mean to the data points always sum to

Zero

To calculate the arithmetic mean

all of the data points must be added together, then divided by the number of data points.

A unit-free measure of dispersion is

coefficient of variation.

The skewness coefficient can be used to

compare two samples with different measurement units. compare one sample to a known reference distribution.

The correlation coefficient values

fall between -1 and +1, inclusive.

The interquartile range of a data set

is calculated by subtracting the first quartile from the third quartile represents the middle 50% of the data.

The correlation coefficient describes the degree of ________ between two _________ variables.

linearity; quantitative

The average of the absolute differences between the values of the data set and the mean is the

mean absolute deviation

The summary measures for grouped data are

only approximate values.

A measure used to gauge the position of items within a data array is

standard deviation.

If the midhinge > median

the data are skewed right.

Generally, skewness can be assessed by comparing

the mean and median.

When calculating a mean for grouped data,

the midpoint of each bin is used to approximate the individual values in that bin.

Accuracy of grouped estimates depends on

the number of bins. the distribution of data within the bins. the bin frequencies.

Nadia purchased 400 shares of XYZ stock at $20 per share. When the stock decreased in value to $16 a share, Nadia purchased 600 more shares of XYZ stock. The weighted average price per share that Nadia paid for XYZ stock is:

$17.60

If the revenue over a four year period was $2000, $2000, $3000, and $5000, what is the geometric mean revenue? Round to a whole number.

$2783

Standard deviations can be compared

- For data sets with the same measurement units. - For data sets with similar magnitude provided the measurement units are the same.

Place the steps in order, from beginning to end, to calculate a mean for grouped data.

1. Find the midpoint for each class of grouped data. 2. Multiply the midpoint of each class by the number of observations in its class 3. Sum the products of the midpoints and observations. 4. Divide by the total number of observations.

Place the steps for using the method of medians in finding quartiles in the proper order.

1. Sort the observations. 2. Find the median for the entire data set, Q2. 3. Find the medians of the data values above and below Q2.

Calculate the standardized score for the following data value. Assume the mean = 100 and the standard deviation = 25: x = 60, z =

1.6

The sample standard deviation of the data set 3, 4, 5, 6, and 7 is

1.6

A certain value has a standardized score = 1.75. How many standard deviations from the mean does this value fall?

1.75

For a given normal distribution, the range is 60. Assuming the distribution is bell-shaped, the estimated standard deviation =

10