Wk 1: Ch. 4: Descriptive Statistics

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. $3000. $2500

$2783.

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

-1.6

The variance measures the average squared __________ from the ___________.

1. Deviations. 2. Mean.

Click and drag on elements in order: Place the steps in order, from beginning to end, to calculate a mean for grouped data. Sum the products of the midpoints and observations. Multiply the midpoint of each class by the number of observations in its class. Divide by the total number of observations. Find the midpoint for each class of 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.

Click and drag on elements in order: Place the steps for using the method of medians in finding quartiles in the proper order. Find the median for the entire data set, Q2. Find the medians of the data values about the below Q2. Sort the observations.

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

Suppose a data set has 80 data points. A 5% trimmed mean would be calculated by removing ______ the highest values and the ___________ lowest values. (Please enter one word per blank. Round the values to the nearest whole numbers.)

1. four 2. four

Numbers that summarize a sample of data are called ________ and numbers that summarize populations are called _________.

1. statistics 2. parameters

A certain value has a standardized score = 1.75. How many standard deviations from the mean does this value fall? a) Cannot tell without knowing the mean. b) Cannot tell without knowing the value of the standard deviation. c) 1.75. d) 3.75.

1.75

For a given normal distribution, the range is 60. Assuming the distribution is bell-shaped, the estimated standard deviation = _________. (Round the value to the nearest whole number.)

10

The maximum value of a data set is 200 and the minimum value is 80. The midrange is equal to ___________.

140

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? 75. 15. 85. 25

15

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 $ ___________ (use 2 decimal places).

17.60

The midhinge for a data with Q1 = 10 and Q3 = 45 is ________.

27.5

A company sold 1000 units in its first year of operation, 1400 units in its second year of operation, and 1680 units in the third year of operation. The average growth rate of the company's sales for years one to three is %. __________ (Round your final answer to a decimal answer with four places and then convert to % with 2 decimals)

29.61%

In general, a data point is considered an outlier if it falls more than __________ standard deviations away from the average.

3

Quartiles divide the data into ________ (choose a number) equal parts.

4

If a company sold 1000 units in its first year of operation, and 1400 units in its second year of operation, then the growth rate of the company's sales is _________%.

40%

If the median price for a home is $200,000, then ________ % of homes cost less than $200,000.

50

For the data set 4, 5, 6, and 9, the arithmetic mean is a) 6.5. b) 5.5. c) 6. d) 7.

6.

Using Chebyshev's Theorem, at least __________ % of observations should fall within 2.5 standard deviations of the mean.

84 %

Select all that apply: 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 observed value contradicts the researcher's intuition about the population under study. If the data point was typed incorrectly into the spreadsheet. If the observed value has a standardized score = 3.14 but there is no indication the value is in error.

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. It is easy to calculate. It is the difference between the highest and lowest values.

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. It is halfway between the lowest and highest values. It is easy to calculate. It is useful when you have only the maximum and minimum values of a data set.

It is robust to outliers.

__________ refers to the relative length of distribution tails.

KURTOSIS

Which shape matches the mean and median relationship? Left skewed: Right skewed: Symmetrical: (mean > median) (mean = median) (mean < median)

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

Match the following terms with their meaning: Mesokurtic: Platykurtic: Leptokurtic: (A flatter distribution than normal with heavier tails). (Normal bell-shaped distribution). (A sharply peaked distribution with thinner tails).

Mesokurtic: (Normal bell-shaped distribution). Platykurtic: (A flatter distribution than normal with heavier tails). Leptokurtic: (A sharply peaked distribution with thinner tails).

Find the first and third quartiles from the following data set using the method of medians: 2, 3, 3, 5, 6, 8, 12. a) Q1 = 3, Q3 = 8. b) Q1 = 5, Q3 = 12. c) Q1 = 3, Q3 = 7. d) Q1 = 2.5, Q3 = 10.

Q1 = 3, Q3 = 8.

When comparing two data sets with different units of measurement, what is the relative measure of dispersion? The standard deviation. The coefficient of variation. The range.

The coefficient of variation

Which of the items below describes the usefulness of a standard deviation? To gauge the relative position of data values within the data set. To help estimate the mean. To compare variables with different units of measure. To determine the median of the data set.

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

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

True

The trimmed mean can mitigate the effect of outliers. True false question.

True

The arithmetic mean is the average of a data set. True. False.

True.

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 false question.

True.

Select all that apply: Which of the following statements is true? Two data sets could have the same mean but different standard deviations. If two data sets have different means they must have different standard deviations. If two data sets have the same mean they must have the same standard deviation. Two data sets could have different means but the same standard deviation.

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

MAD, a measure of dispersion, stands for mean _________ deviation.

absolute

To calculate the arithmetic mean all the data points, except outliers must be added together, then divided by the number of data points. all the data points are multiplied together, then divided by the number of data points. all of the data points must be added together, then divided by the number of data points. the most frequently occurring data point is selected.

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

When there is uneven distributions of grouped data within bins the effects will tend to ___________ out unless there is systematic skewness.

average

When monitoring a process distribution, both the _________ and the ___________ must be tracked.

average, variation

A unit-free measure of dispersion is a) standard deviation. b) coefficient of deviation. c) range. d) coefficient of variation.

coefficient of variation.

Select all that apply: The skewness coefficient can be used to compare standard deviations. compare two samples with different measurement units. compare means. compare one sample to a known reference distribution.

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

The standardized value of the covariance is called the __________ (one word) coefficient.

correlation

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

covariance

When a data set is symmetrical, the mean and median are approximately the ___________ . (Please enter one word in the blank.)

equal

The correlation coefficient values are always greater than zero. can be any value. fall between -1 and +1, inclusive. are always less than zero.

fall between -1 and +1, inclusive.

Select all that apply: Standard deviations can be compared for data sets with different measurement units. for data sets with the same measurement units but greatly different magnitudes. for data sets with the same measurement units. for data sets with similar magnitude provided the measurement units are the same.

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

The ___________ mean is the multiplicative average of a data set.

geometric

The correlation coefficient describes the degree of ________ between two _________ variables. linearity; quantitative. nonlinearity; quantitative. linearity; qualitative. nonlinearity; qualitative

linearity; quantitative

The average of the absolute differences between the values of the data set and the mean is the arithmetic mean. mean absolute deviation. standard deviation. geometric mean.

mean absolute deviation

The best measure of central location for a numerical data set when the data set contains outliers is the ___________. (Enter one word in the blank.)

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 mean. outlier. median. mode.

median

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

median

Select all that apply: The second quartile is also the: mean. 50th percentile. median. mode.

median. 50th percentile.

The __________ is the measure of center that identifies the most frequently occurring value in the data set.

mode

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

mode

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

mode.

Which measure of center is the most frequently occurring value? a) mode. b) median. c) mean.

mode.

When estimating sigma using the following formula: xmax−xmin / 6 , one is assuming the distribution is Bimodal. Normal. Highly skewed. No assumption on the distribution

normal

The summary measures for grouped data are only approximate values. are more accurate than the summary measures for raw data. the same as the summary measures if the data was not aggregated.

only approximate values.

The __________ measures the difference between the largest and smallest values in a data set.

range

A measure used to gauge the position of items within a data array is standard variation. standard deviation. relative variation. relative deviation.

standard deviation

If the midhinge > median a) the data are symmetrical. b) the data are skewed right. c) the data are skewed left.

the data are skewed right.

Select all that apply: Accuracy of grouped estimates depends on the distribution of data within the bins. the number of bins. the data magnitude. the bin frequencies.

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

Generally, skewness can be assessed by comparing the mean and standard deviation. the mean and the range. the mean and median. the mean and mode.

the mean and median.

When calculating a mean for grouped data, each individual value is added together and divided by the sample size. the lowest values for each bin are added together and divided by the number of classes. means cannot be calculated for grouped data. the midpoint of each bin is used to approximate the individual values in that bin.

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

The average squared difference of data values from their mean is the standard deviation. mean absolute deviation. variance. range.

variance.

Multiplying data values by a fraction (where the fractions add to 1) and summing results in a __________ mean.

weighted

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

zero

Match the data characteristic to what it describes. Center: Variability: Shape: (symmetrical or skewed) (spread of data values or dispersion) (Typical or middle value; where the data values are concentrated)

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

Select all that apply: 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? The mode. Chebyshev's Theorem. The empirical rule - assuming a normal distribution. Percentiles

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

The standard deviation can be a negative value. True false question.

FALSE

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

False