Chapters 1-4 Learnsmart

Range, Variance, Standard Deviation

which of the following are used to measure dispersion? Check all that apply.

Frequency

The number of observations in each class is called the class_______?

class midpoints

In a frequency polygon the points are plotted at the intersection of the class frequencies and the:

Positively skewed

In a particular country most of the households have an annual income of about $20,500. Five percent of the households have incomes above $500,000. The distribution of income is:

50 because 250-200=50

In the cumulative frequency polygon show, about how many observations are there between a value of 200 and 250?

descriptive statistics and inferential statistics

The two categories of statistical study are:

counting the number of observations less than the upper limit of the class.

The value how on the vertical axis of a cumulative frequency polygon for a particular class is found by:

9; add up all the numbers, then divide by how many numbers there are = 45/5

Calculate the mean for the following sample of data: 12, 15, 6, 4, 8

A grouping of qualitative data into classes showing the number of observations in each class.

Which of the following best describes a frequency table?

The approximate number of observations, The shape of the distribution, The concentration of the data, The spread of the data.

Which of the following can be observed from a histogram? Check all that apply.

2. yesterdays share price for proctor and gamble stock 3. median price of house in detroit 4. number of home runs in last year's world series

Which of the following examples of statistics? Select all that apply.

It can directly compare two or more frequency distributions.

Which of the following features is an advantage that the frequency polygon has over the histogram?

The mean of a sample

Which of the following is a statistic?

Both use mutually exclusive classes.

Regarding frequency tables and frequency distributions, which one of the following is true?

It is in the same units as the data.

Of the following, which one is an advantage of the standard deviation over the variance?

equal to one

Suppose a cumulative relative frequency distribution is used to summarize n observations. The cumulative relative frequency for the class class will always be?

K is the smallest number such that 2k>n.

A useful way to determine the number of classes (k) in a frequency distribution of n items is the "2 to the k rule". Which of the following correctly describes this rule?

The miles per gallon for a particular model of car.The weight of a Siamese cat.

Identify all of the following items which are quantitative variables?

Symmetrically distributed

In the library of a small town, the mean cost of new books is the same as the median and mode cost of new books. The distribution of book costs is?

2 years

Suppose the sample variance is calculated for a data set containing the ages, in years, of a sample of visitors to the zoo and it is 4. What is the standard deviation?

discrete and continuous

What are the two types of quantitative variables?

A characteristic of a population.

What is the definition of "parameter?"

For the sample variance, the sample mean is used in place of the population mean. For the sample variance, the denominator is the number of observations minus 1.

How is the formula for the sample variance different from that of the population variance? Select all that apply.

(11, 14, 16, 1, 12, 15, 17)

The median would be a better measure for the center of the data for of which of the following data sets?

14.67

What is the variance of the following sample data?2, 6, 2, 10

the arithmetic mean of the squared deviations from the mean.

What is variance?

Ratio

What level of data gives you the most information of the observation?

There is only one mean for a set of data All the values in the data are used in calculating the mean. The sum of the deviations of each value from the mean is zero. Expressed symbolically:Σ(x−xbar)=0

Which of the following are important properties of the arithmetic mean? Check all that apply.

The value of the observation that appears most frequently.

Which of the following statements best defines the mode?

Medians can be calculated from ordinal-level data, but means can't

Which of the following is true regarding medians and means?

Choosing data that supports your conclusion

Which of the following is NOT part of the science of statistics?

Brand of newly purchased TV

Which of the following represents data recorded at the nominal level?

Use samples that represent only a desired part of the population. Report only those statistics that support his conclusions. Remove outliers that bias the data too far in one direction.

Which of the following are not proper and ethical activities for a statistician in working with data? Select all that apply.

-it has all the properties of interval -level data-the zero point of the data is meaningful -the ratio between two measures is meaningful

Which of the following are properties of ratio level data? Choose all that apply.

The area of a slice for a class relative to the whole pie should match its relative frequency.

Which of the following is true about pie charts?

Interval level data ordinal level data ratio level data

Which of the following kinds of data can be used to find the median value? select all that apply

It allows us to compare the spread in two or more distributions.

Which of the following statements are reasons to study dispersion of data? Select all that apply.

9 it is the maximum minus the minimum. 12-3=9

What is the range for the following set of data?4,12,5,3,7,8,9

2.83

What is the standard deviation of the following population data? 3,1,2,9,5

N: 5 M: 4 SS: 34 s2 = SS⁄(N - 1) = 34/(5-1) = 8.5 s = √s2 = √8.5 = 2.92

What is the standard deviation of the following sample data?7,6,2,0,5

The midpoint of the data when it is arranged in order.

Which of the following accurately describes the median of a set of data?

It uses all of the values in the data, not just two.

Which of the following are advantages of the variance compared to the range?

Histogram and Frequency Polygon.

Which of the following graphs are used to summarize quantitative data? Select all that apply.

12.50

what is the variance of the following population data?

the data may be bimodal there may be no observation that occurs more than once the most frequent observation is much higher or much lower than most of the data values.

which of the following are reasons why the mode would NOT be the good choice of measure for the describing the center of a set of data? check all that apply

it measure squared distance from the mean

which of the following are true regarding the variance?

$25

Suppose a frequency distribution has the following consecutive classes: $20 up to $30 $30 up to $40 $40 up to $50 What is the class midpoint for the first class?

10

Suppose you are trying to summarize a data set a maximum value of 70 and a minimum value of 1. If you have decided to use seven classes, which one of the following would be a reasonable class Interval?

75%

The average age of undergraduate students at Grand Canyon University is 44. If the standard deviation is 4, what percentage of undergraduate students are between 36 and 52 years old?

K is the number of standard deviations, greater than 1, within which that proportion of observations will be found.

chebshev's theorem states that the proportion of values is at least 1-1k what is the meaning of k?

0

if all the data are the same then the population variance will be what?

the square root of sample variance

sample standard deviation is:

-there are gaps between the values of this variable -it can be used to count items, in which care it can only have integral values -it can assume only certain values within a range

Which of the following are attributes of a discrete quantitative variable? Choose all that apply

The denominator of the weighted mean is always the sum of the weights. It is a special case of the arithmetic mean. It is used when there are several observations of the same value.

Which of the following statements are true of the weighted mean? Select all that apply.

Only two values from the data set are used. It may be unduly influenced by the especially small value. I may be unduly influenced by an unusually large value.

Which of the following statements describe weaknesses of the range as a measure of dispersion?

Nominal Ordinal Interval Ratio

Which of the levels of measurement can the mode be used? Select all that apply.

Raw data are simply a listing of data before summarizing it.

Which one of the following is true regarding raw data?

An average

Which one of the following would be an example of a measure of location?

Placing excess interval width equally in the two tails of the distribution. Rounding the class interval up.

Which two of the following practices is commonly used in setting class limits for a frequency distribution?

Divide the sum of the values in the population by the number of values in the population.

How do you find the population mean for a set of data?

A good working knowledge of statistics is useful to organize and summarize information

How does statistics help us understand large amounts of numerical information?

the fraction of percentage of observations in each class interval

Relative frequencies are?

The 6th value in the ordered listing of the data.

Suppose a data set includes 11 values. Which one would be the median?

The more spread out the data is.

The larger the population variance is for a data set,

When the data set includes one or two very large or very small values.

What characteristic of a data set makes the median the better measure of the center of the data than the mean?

interval, ordinal, nominal, ratio

What is the level of data to the following observations: shoe size, movie ratings, the types of fruit in a grocery store, stock prices

Shows the proportion of observations less than each class upper limit.

A cumulative relative frequency distribution?

a histogram

A frequency polygon shows the shape of a distribution and is similar to:

68% Plus or minus one standard deviation 95% Plus or minus two standard deviations 99.7% Plus or minus three standard deviations

According the the empirical rule, a certain percentage of observations will be found within a specific number of standard deviations of the mean for a normal distribution. match the percentage of observations to the number of standard deviations.

1. Decide on the number of classes. 2. Determine class width. 3. Set individual class limits. 4. Tally the number of observations in each class.

Place the following steps used in constructing a frequency distribution into correct order.

- it can take on any value within a range of values - there are no required gaps between values (gaps may exist, but they are not required by the nature of the variable) - it is typically the result of measuring something (measurements can result in fractional values)

Which of the following are attributes of a continuous quantitative variable? choose all that apply

There should be gaps between bars, Bar charts are used for qualitative data, Plotted rectangles should be the same width.

Which of the following are characteristics of bar charts? Select all that apply.

- creating a pie chart to show the majors of students in your business stats class - calculating summary measures of the prices of houses sold in Las Vegas in January

Which of the following are examples of descriptive statistics? select all that apply

Chebyshev's theorem works for symmetrical, bell-shaped distributions. The Empirical Rules gives more precise answers for the symmetrical, bell-shaped distribution

Which of the following is true regarding the application of Chebyshev's theorem and the Empirical Rule? Check all that apply.

The relative frequency is found by dividing the class frequencies by the total number of observations.

Which of the following operations is true regarding relative frequency distributions?

the formulas are functionally the same, but 'n' (the sample size) is used instead of 'N' (the population size) The greek letter mu, u, is used to represent the population while, x-bar is used for the sample mean

How does the formula for the sample mean differ from the formula for population mean?

Median Mode

Which of the following are good measures of the center of an income distribution in a country where most of the households have annual incomes of about $40,000, but a small number of households have incomes above $1,000,000? Select all that apply.

A statistical report requires objective and honest communication of results.

which of the following statements represents an ethical approach to the use of statistics?

Statistical knowledge is needed to understand the world and be conversant in your career - Data is everywhere, and statistics is needed to understand it - statistics is used to make personal and professional decisions

Which of the following are true with regard to the importance of studying statistics? Select all that apply.