Ch 4, Descriptive Statistics

In a neighborhood there are five houses listed for sale for the following amoints: $250,000; $275,000; $280,000, $295,000, and $515,000. What is the best measure of center for the price of a house on the neighborhood?

Median

The second quartile is also the

Median 50th percentile

Which of the following are measures of center of a data set?

Median Mode Mean

Match the following terms with their meaning Mesokurtic= Platykuric= Leptokurtic=

Mesokurtic= Normal bell-shaped distribution Platykuric= A flatter distribution than normal with heavier trails Leptokurtic= A sharply peaked distribution with thinner trails

Which of the following correlation coefficients indicate the strongest inverse relationship between two variables?

-0.87

When the correlation coefficient approaches the value ____, it indicates that there is a weak relationship between the two variables.

0

In which of the following data sets would the arithmetic mean not be a good measure of central locations

0, 8, 8, 9, 10

If a data set has a standard deviation of 4 units and a mean of 10 units, the coefficient of variation is

0.4 (4/10)

Place in order, from beginning to end, the steps to calculate the mean absolute deviation

1. Calculate the arithmetic mean for the data set 2. Find the absolute difference between each data set value and the mean 3. Sum the absolute difference 4. Divide the sample (or the population) size

Place the following steps in order, from beginning to end, to create a box plot

1. Calculate the five-number summary 2. Plot the five-number summary values in numerical order on a horizontal or vertical axis 3. Draw a box from Q1 to Q3 then add lines from Q1 to the minimum value and Q3 to the maximum value

Place the for 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 median for the value above the below Q2

Place the step 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 median of the data values above and below Q2.

The population standard deviation of the data set 3, 4, 5, 6, and 7 is ______ (Round your final answer to 1 decimal place)

1.4

Inner fences on a boxplot are ____ x IQR above Q3 and below Q1. Outer fences are ___ x IQR above Q3 and below Q1.

1.5 3

The sample standard deviation of the data set 3, 4, 5, 6, and 7 is _____ (Round your final answer to 1 decimal place.)

1.6

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

1.6.

A certain value has a standard score = 1.75. How man y standard deviation from the mean does the value fall? Is the value greater than or less than the mean

1.75 greater than the mean

A certain value has a standardized sore = 1.75. how many standard deviations from the mean does this value fall? Is the value greater than or less than the mean?

1.75. Greater than the mean

Randall Racer runs the 100 meter dash in an average time of 10.4 seconds with a standard deviation of 0.1 seconds. If Randall's time are normally distributed, we have a 99.7% expectation that his finishing time for his race will be grayer than ____ seconds.

10.4

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

140

Nadia purchased 400 shares of XYZ stocks 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 data with Q1 = 10 and Q3 = 45 is _____.

27.5

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

If a company sold 1000 units in its first year of operation, and 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 the final answer to a decimal answer with four places and then convert to % with 2 decimals).

29.61%

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 sales is

40%

The mean for the data sets 6, 4, 9, 5 is

5.5

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

6

The range of the data set: 2, 5, 5, 7, and 10 is

8

Using Chebyshev's Theorem at least ____ % of observations should fall within 2.5 standard deviation of the mean

84

The empirical rule states that approximately_____ of observations will fall within two standard deviation of the mean.

95%

The owner of BevaMart wants to study the relationship between the temperature and hot chocolate sales. The owner compared the covariance between temperature and hot chocolate sales to be -81.46. Based on the covariance, which option best describes the liner relationship between temperature and hoy chocolate?

As the temperature increases, hot chocolate sales decrease.

When calculating a percentile, the first step is to arrange the data set in

Ascending order. (from least to greatest)

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

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

The skewedness coefficient can be used to

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

The skewness coefficient can be sued to

Compare two samples with different measurements units Compare one sample to a known reference distribution.

The correlation coefficient values

Fall between -1 and +1, inclusive.

True or False: Summaries of grouped observations are just as accurate as summaries of a data set of individual observations.

False

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

False

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

Find the midpoint for each class of grouped data Multiply the midpoint of each class by the number of observations in its class Sum the products of the midpoint and observations Divide by the total number of observations

Standard deviation can be compared

For data sets with the same measurement units and similar magnitude. For data sets with the same measurement units.

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.

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.

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

It is robust to outliers

Which shape matches the mean and median relationship Lest skewed= Right skewed= Symmetrical=

Lest skewed= Mean < Median Right skewed= Mean > Median Symmetrical= Mean = Median

When estimating sigma using the following formula: (Xmax - Xmin) / 6, one is assuming the distribution is

Normal

The summary measures for grouped data are

Only approximate values

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

Q1= 1 Q3= 8

Which of the following characteristics can be seen on a boxplot?

Shape Variability Center

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

The coefficient of variation

If the midhinge > median

The data are skewed right

Accuracy of grouped estimates depend on

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

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

The first quartile The largest value

Generally, skewness can be assessed by comparing

The mean and median

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

The smallest value The third quartile The second quartile

Two widely used measure of dispersion are

The variance and the standard deviation

The mode for the data set: 4, 5, 6, 9 is

There is no mode

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

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

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

True

When monitoring a process distribution, both the _____ and the _____ must be tracked

center variability

The standard value of the covariance is called the ___ (one word) coefficient.

correlation

The variance measures the average squared _________ from the ______

deviation mean

When a data set is symmetrical the mean and median are approximately ____

equal

Suppose a data set has 80 data points. A 5% trimmed mean would be calculated by removing the _____ highest values and the ______ lowest values.

four four

If the covariance is positive, then as one variable increases the other variable will generally

increase

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

mean absolute deviation

Generally, the ______ is the best measure of center when outliers are present.

median

Generally, the _______ is the best measure of center when outliers are present.

median

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

median

An owner of a grocery store wanted to determine the brands of soda that consumers purchase at the store. When summarizing the data about soda brand purchase the meaningful measure of center is the

mode

The _____ is the measure of center that identifies the most frequency occurring value in the data set.

mode

When summarizing a qualitative data set the ______ is the best measure of central location.

mode

When a quantitative data set is significantly affected by ______, then the arithmetic mean is usually not a good measure of central location.

outliers

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

range

The square root of the average squared deviation of data values from their mean is known as the_______ _______.

standard deviation

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

three

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

variance

Multiply data values by a fraction (where the fraction add to 1) and summing results in a _____ mean.

weighted