Test 1
What does the frequency polygon have an advantage over to a histogram?
It allows us to compare directly two or more frequency distributions
How do you tell positive or negative skewness in a box plot?
Longer of the whiskers
_____ can be computed for an open-ended frequency distribution if the ______ does not lie in an open-ended class.
Median
_____ is not affected by extremely large or small values and is therefore a valuable measure of central tendency when such values occur.
Median
What must you know to develop a box plot?
Minimum Quartile 1 Median Quartile 3 Maximum
The ____ is the value of the observation that appears most frequently.
Mode
_____ is a chart that shows the proportion or percent that each class represents of the total number of frequencies.
Pie charts
_____ is used for relative frequency.
Pie charts
Is bar charts used for qualitative or quantitative data?
Qualitative data
What are the measures of dispersion?
Range Mean deviation Variance and Standard Deviation
Class frequencies can be converted to ______ _____ ________ to show the fraction (which can be converted to %) of the total number of observations in each class.
Relative class frequencies
The ________ is the only measure of central tendency where the sum of the deviations of each value from the mean is zero.
arithmetic mean
What is the most widely used measure of location and requires the interval scale?
arithmetic mean
The ____ the dispersion, the ____ you certain you are.
bigger less
What does a histogram and frequency polygon have in common?
both provide quick picture of the main characteristics of the data (highs, lows, points of concentration, etc.)
Frequency polygon consists of line segments connecting the points formed by the intersections of the ______ and the ______.
class midpoints class frequencies
What is a second reason for studying the dispersion in a set of data?
compare the spread in two or more distributions
Every set of what levels of measurement have a median?
ratio-level interval-level ordinal-level
The mean is always ______ unless it gets negatively skewed.
right
For ungrouped data, the _______ is the sum of all the sample values divided by the number of sample values
sample mean
A frequency polygon also shows the _____ of a distribution and is similar to a ______.
shape histogram
The ____ is the most widely used measure of dispersion.
standard deviation
What advantage does the histogram have?
depicting each class as a rectangle, with the height of the rectangular bar representing the number in each class
How do you convert a frequency distribution to a relative frequency distribution?
each class frequency is divided by total number of observations
Frequency table is a grouping of _______ data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class.
qualitative
Stem-and-leaf display condenses qualitative or quantitative information?
quantitative
_______ is a grouping of quantitative data into mutually exclusive categories showing the number of observations in each class.
Frequency distribution
What has a wide application in business and economics because we are often interested in finding the percentage changes in sales, salaries, or economic figures, such as the GDP, which compound or build on each other?
Geometric Mean
What is useful in finding the average change of percentages, ratios, indexes, or growth rates over time?
Geometric Mean
______ for a frequency distribution based on quantitative data is very similar to the bar chart showing the distribution of qualitative data.
Histogram
What are the three graphic forms of a frequency distribution?
Histograms Frequency polygons Cumulative frequency distributions
What is the rule to determine number of classes (k)?
"2 to the k rule" 2^k > n
What are the major characteristics of arithmetic mean?
-all values are used -it is unique -the sum of the deviations from the mean is 0 -It is calculated by summing the values and dividing by the number of values
The relative frequency captures the relationship between what?
-class total -total number of observations(% or fraction)
What are the four shapes commonly observed in skewness?
-symmetric -positively skewed, Mode, Median, Mean -negatively skewed, Mean, Median, Mode -bimodal
Pearson's Coefficient of Skewness
3(mean-median)/SD
Why study dispersion?
A measure of location, such as the mean or the median, only described the center of the data. It is valuable from that standpoint, but it does not tell us anything about the SPREAD of the data.
_______ is a graph in which the classes are reported on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are proportional to the heights of the bars.
Bar Charts
The number of observations in each class
Class frequency
The ______ is obtained by subtracting the lower limit of a class from the lower limit of the next class
Class interval (i)
A point that divides a class into two equal parts. This is the average of the upper and lower class limits.
Class midpoint
What is used to study the relationship between two variables when one or both are nominal or ordinal scale?
Contingency table
________ is a table used to classify observations according to two identifiable characteristics.
Contingency table
What is Step 5 for constructing a frequency table?
Count the number of items in each class
What is the first step in constructing a frequency tWhaaable?
Decide on the number of classes
Pearson's Coefficient of Skewness
Defines skewness as a multiple of the standard deviation of a set of values. Negative values signify a data set with greater weight given to values below the median while positive values signify the opposite.
Frequency tables uses _____ statistics.
Descriptive
What is step 2 in constructing a frequency table?
Determine the class interval or width
_____ groups the data as little as possible and the identity of an individual observation is not lost
Dot plot
One graphical technique we use to show the relationship between variables is called a _________
Scatter diagram
What is Step 3 for constructing a frequency table?
Set the individual class limits
The major advantage to organizing the data into frequency distribution is that we get a quick visual picture of what?
Shape of distribution
What is Step 4 for constructing a frequency table?
Tally the vehicle selling prices into the classes
What does the interquartile range describe?
The middle 50% of the observations
Besides central location (mean, median, mode) and data dispersion (range, standard deviation), what is another characteristic of a set of data?
The shape
What is the formula for determining the class interval?
i >= (H-L)/k
A scatter diagram requires that both of the variables be at least _____________.
interval scale
Every set of what levels of measurement have a mean?
interval-level ratio-level
The geometric mean will always be _____ than or equal to the arithmetic mean.
less
Alternative ways of describing spread of data include determining the ________ of values that divide a set of observations into equal parts. These measures include what?
location quartiles deciles percentiles
The _____ is affected by unusually large or small data values.
mean
A set of data has a unique ______
mean or median
mode>median>mean
negative skewness, skewed to the left
mode<median<mean
positive skewness, skewed to the right
What is the advantage of the stem-and-leaf display over a frequency distribution?
the identity of each observation is not lost
For ______ data, the population mean is the sum of all the population values divided by the total number of population values
ungrouped
Relative Dispersion
unitless and is used to compare the variability of two different distributions that have different measures or values
Weighted mean equation
x bar= E(w*x)/Ew