Statistics Test 1

For a set of data, the mean is 50 and the standard deviation is 10. In the raw data, one of the observations is equal to 74. After the data are standardized, what will be the standardized value of this observation?

+2.4

A sample of 13 monthly sales figures (in thousands of dollars) are: 10, 6, 5, 10, 9, 7, 10, 9, 6, 8, 9, 6, and 6. The mean absolute deviation (MAD) of these numbers is? Show three decimal places.

1.633

A sample of 13 monthly sales figures (in thousands of dollars) are: 10, 6, 5 10, 9, 7, 10, 9, 6, 8, 9, 6, and 6. The standard deviation of these numbers is? Show three decimal places.

1.830

The grades on a chemistry exam for a sample of 40 students are as follows: 47, 84, 62, 57, 82, 68, 64, 74, 83, 71, 67, 42, 54, 91, 76, 56, 79, 71, 79, 51, 62, 86, 61, 54, 68, 69, 81, 36, 58, 75, 77, 65, 41, 94, 59, 68, 48, 55, 38,63. Calculate the percentage of grades that are between 80 and 90.

12.5%

The largest value in a set of data is 160, and the smallest value is 70. If the resulting frequency distribution is to have six classes of equal width, what will be the class interval?

15

A sample of 15 observations has a standard deviation of 4. The sum of the squared deviations from the sample mean is:

224

A stem-and-leaf display describes two-digit integers between 20 and 80. For one of the classes displayed, the row appears as 5|246. What numerical values are being described?

52, 54, and 56

The Empirical Rule states that the percentage of observations in a data set (providing that the data set has a bell-shaped and symmetric distribution) that fall within one standard deviation of their mean is approximately:

68%

The average score for a class of 25 students was 75. If the 15 female students in the class averages 70, then the male students in the class averaged:

82.5

A student scores 89, 72, 93, and 84 on four exams during the semester and a 96 on the final exam. If the final is weighted double and the four others weighted equally, the students final average is? Show two decimal places.

88.33

Which of the following sample statistics is a measure of spread (dispersion)?

Sample Standard Deviation

The midway point between the upper and lower class limits for a frequency distribution is known as the:

class mark

In cross-tabulation:

data are represented in a table showing how many people or items are in combinations of categories, we can identify possible relationships between the variables.

The ______ is a graphical display providing cumulative values for frequencies, relative frequencies, or percentages.

ogive

In a scatter diagram, data are represented as:

pairs of unknown values of two variables, one being referred to as independent and the other, dependent.

The relative frequency distribution describes the:

proportion of observations that fall within each class

A survey asks the respondent to indicate the number of cats in the household. The variable in question is an example of which type?

quantitative, discrete

The difference between the mean of a data set and the individual values of that set is known as the:

residual

When data are collected in a statistical study for only a portion or subset of all elements of interest we are using a:

sample

What are 5 techniques applicable to quantitative data?

the data array, frequency distributions, stem-and-leaf display, scatter diagram and Dotplot

The difference between a histogram and a bar chart is that:

the histogram reflects quantitative data while the bar chart represents qualitative data, the adjacent rectangles in a bar chart have a gap while those in a histogram usually do not.

The measure of central tendency that is most affected by extreme values is the:

the mean

The measure of central tendency that is least affected by extreme values is the:

the median

The following stem-and-leaf output has been generated by Minitab: N=10 2 -1 53 4 -0 97 (2) -0 65 4 0 3 3 0 6 2 1 3 1 1 8 What does this say about the mean, mode, and negatives?

this data set has a mean that is negative, this data set has a median less than -0.5, there is no modal class, this data set has six negative values

The class interval is the:

width of each class

In a positively skewed distribution, the mean is :

greater than the median and the median is greater than the mode

True or False: The Empirical Rule states that approximately 68% of the observations in any distribution will fall within one standard deviation of the mean.

False

True or False: The appropriate methods for representing the data do not depend on whether the variable of interest is quantitative or qualitative.

False

True or False: The midrange is the average of the two middle data values.

False

True or False: The sample statistic is a characteristic of the sample that the population parameter attempts to estimate.

False

True or False: The set of classes in the frequency distribution should be selected so that any give value falls into at least one category.

False

True or False: The sole purpose of the U.S. Census Bureau is to simply count how many people live in the United States.

False

Statistic

A summary measure that is computed from a sample to describe a characteristic of the population is called:

Parameter

A summary measure that is computed using the entire population is called:

continuous

Continuous measures are measured along a continuous scale which can be divided into fractions, such as temperature. Continuous variables allow for infinitely fine sub-division, which means if you can measure sufficiently accurately, you can compare two items and determine the difference.

True or False: A discrete quantitative variable can take on a value at any point along an interval.

False

True or False: ATP singles ratings for tennis players rank Rafael Nadal as 2 and Rodger Federer as 1. This is an example of an interval scale.

False

True or False: In a raw data listing, data are listed in increasing or decreasing numerical order.

False

True or False: In inferential statistics, we simply summarize and describe the data we've collected.

False

True or False: In the nominal measurement scale, numbers represent "greater than" or "less than" measurements, such as rankings or preferences.

False

True or False: Measures of dispersion describe typical values in the data.

False

True or False: Quantitative variables usually represent membership in groups or categories.

False

Is this descriptive or inferential statistics: The Alcohol, Tobacco and Firearms Department reported that Houston had 1,791 registered gun dealers in 1997.

Descriptive Statistics

discrete

Discrete variables are measured across a set of fixed values, such as age in years (not microseconds). These are commonly used on arbitrary scales, such as scoring your level of happiness, although such scales can also be continuous.

True or False: Six classmates told you their scores on the last statistics exam. Based on this information, you conclude that the average exam score for the entire class was 82. This is an example of descriptive statistics.

False

ratio scale

In a ratio scale, numbers can be compared as multiples of one another. Thus one person can be twice as tall as another person.

Is this descriptive or inferential statistics: Based on a sample of 500 subscribers, a local cable system estimates that forty percent of its subscribers watch a premium channel at least once per day.

Inferential Statistics

Interval data

Interval data (also sometimes called integer) is measured along a scale in which each position is equidistant from one another. This allows for the distance between two pairs to be equivalent in some way. ex: My level of happiness, rated from 1 to 10, temperature, in degrees Fahrenheit.

Ordinal

Items on an ordinal scale are set into some kind of order by their position on the scale. This may indicate such as temporal position, superiority, etc. ex: The first, third and fifth person in a race.

An automobile insurance agent believes that company A is more reliable than company B. Which scale of measurement does this information represent?

Ordinal

Range

The difference between the highest and lowest values in the sample is known as the sample:

Median

The statistic that describes the midpoint of the data which has just as many values above it as below it is known as the sample:

Which of the following is most likely a continuous quantitative variable?

The temperature in a room

True or False: A box plot shows the median but not the mean of a set of data.

True

True or False: Compared to the frequency distribution, the stem-and-leaf display provides more detail since it can describe the individual data values as well as show how many are in each group, or stem.

True

True or False: Contingency tables are used primarily for counts involving qualitative data.

True

True or False: Standardized values have no units, even though the original data, the standard deviation, and the mean may each represent units such as dollars, hours, or pounds.

True

True or False: Stating that Wal-Mart's sales increased 6.2% this quarter when compared to last quarter is an example of descriptive statistics.

True

True or False: The box-and-whisker plot is a graphical device that simultaneously displays measures of central tendency and dispersion.

True

True or False: The median is the 5th decile.

True

True or False: The scatterplot can simultaneously show values of two quantitative variables (y, or vertical axis, and x, horizontal axis), such as height (x) and weight (y).

True

A requirement for a frequency distribution is that the set of classes must be mutually exclusive. This means that:

a given data value can fall into only one class

If the coefficient of correlation r is positive, the two variables x and y are:

directly linearly related

The length of the box in the box-and-whisker plot portrays the:

interquartile range

Class limits are:

lower and upper boundaries of each class

Nominal

nominal data are items which are differentiated by a simple naming system. ex: The number pinned on a sports person, a set of countries.