EXST 2201 Lecture Exercises 1-2
Can the standard deviation (σ) be used to find probability? A. Yes, it can with a normal curve. B. Yes, because it is part of a distribution C. No, because the average deviation is used D. No, because spread is not needed to find probability
A
Does the sum of squares (SS) usually get bigger as more data values are added to the data set? A. Yes, because there are more numbers in the data set to sum. B. Yes, because bigger data sets must have bigger sum of squares than smaller data sets C. No, because the new data values could have negative squares D. No, because the sum of squares is adjusted for the number of data values in the data set.
A
How many data values are less than the value of the third quartile (Q3)? A. Three quarters (75%) of the data values B. One third (33%) of the data values C. The middle half (50%) of the data values D. One quarter (25%) of the data values
A
In Step 2: Move to the correct position of finding a percentile (Pk), how is the appropriate move decided? A. If i is an integer, average that and the next higher data values. If i has a decimal, move up to the next higher data value B. If i is an integer, move up to the next higher data value. If i has a decimal, average that and the next higher data values. C. If k/100 is less than 0.5, move down to the next lower data value. If k/100 is greater than 0.5, move up to the next higher data value. D. If i is an integer, average that and the next lower data values. If i has a decimal, move down to the next lower data value
A
In a data set used in statistics (imagine a MS Excel spreadsheet), information about the variables are contained in the columns. A. True B. False
A
In a data set used in statistics (imagine a MS Excel spreadsheet), information for the variables are contained in the columns. A. True B. False
A
In a distribution of a column of data, a statistic for location measures where the middle of the data values lie in a real number line. A. True B. False
A
In statistics, a deviation applies to only one data value. A. True B. False
A
In statistics, the mathematical distance between two numbers is defined as A. Taking the difference between the two numbers B. Sun the two numbers, then divide by 2 C. Taking the difference between the two numbers, then dividing by the spread of the data D. The distance between the two numbers on a real number line found by using a ruler
A
It is known that the science of statistics can determine the relationship between two variables, but that it cannot determine if one variable causes the values in the second variable. What concept makes this statement true? A. The concept of a lurking variable B. The concept of inaccuracy due to using probabilistic data C. The concept of lack of precision in the calculations of the statistics D. The concept of having to use sample information instead of population information
A
Match each characteristic of a distribution with the appropriate statistic for qualitative data. Spread A. Number of categories B. Mode C. Bar chart
A
Match the appropriate set of statistics to the descriptions below. Less affected by extreme values A. Resistant statistics B. Efficient statistics
A
Match the appropriate statistic for a distribution of efficient statistics. Shape A. Histogram B. Mean C. Standard deviation
A
Match the appropriate statistic for a distribution of resistant statistics. Shape A. Boxplot B. Inter-quartile range C. Median
A
Match the following statistics with the characteristic of a column of data that they summarize. Standard deviation or inter-quartile range A. Spread B. Location C. Size
A
Match the two meanings below with their appropriate column titles in a frequency table. Count of the data values in a category A. Frequency B. Relative frequency
A
The Gallup News Service sent out 2,000 questionnaires for survey about climate change. 1,004 people responded to the survey and the others did not. What type of statistical study is this survey? A. This is an observational study B. This is a partial study since only half of the people responded C. This is an ineffective study since it would represent only half of the population D. This is an experimental study
A
The average age of students enrolled in last Fall's engineering class was found to be 24 years of age. What type of statistics does this statement describe? A. Descriptive statistics B. Inferential statistics
A
The first step in doing statistics is always? A. Abstract information from the problem B. Describe the columns of data C. Infer the population values D. Use p-value to make a better decision
A
To find resistant statistics, what must be true of the data set? A. The data values must be ranked from lowest to highest B. The data set must be checked to make certain that no two data values occupy the same position C. The position of the data values must be found in the initial data set D. The data values must be ranked from highest to lowest
A
What characteristic is summarized by the pattern of data values when graphed? A. Shape B. Spread C. Location
A
What is the statistical term for all the squared deviations added together? A. Sum of squares B. Variance C. Standard deviation D. Root mean square
A
What one of the following answers is true about a parameter? A. A constant that gives population information B. A constant that gives sample information C. A variable that gives population information D. A variable that gives sample information
A
When making a histogram for continuous data, a bin is just a range of possible data values. A. True B. False
A
Which of the following answers is NOT an exception when analyzing a histogram? A. Any bimodal shapes B. Any gaps or peaks C. Any patterns or grouping D. Any extreme values
A
A boxplot is used to display the shape of qualitative data. A. True B. False
B
A confidence interval for the age of students enrolled in last Fall's engineering class was found to be (22, 26) years of age. What type of statistics does this statement describe? A. Inferential statistics B. Descriptive statistics
B
A data value close to the mean has a? A. Large deviation B. Small deviation C. No deviation D. Middle deviation
B
A deviation can never equal zero. A. True B. False
B
A shoe store wants to know how much money, on average, their customers spend each visit to the store. Using their store records, they draw a sample of 4.500 customer visits and record the amount spent at each customer visit. The average of this data is calculated to answer the shoe store's question. What is the sample in this example? A. The amount spent in the store at each customer visit B. The 4,500 customer visits recorded C. All shoe store customer visits
B
A shoe store wants to know how much money, on average, their customers spend each visit to the store. Using their store records, they draw a sample of 4.500 customer visits and record the amount spent at each customer visit. The average of this data is calculated to answer the shoe store's question. What is the variable in this example? A. All shoe store customer visits B. The amount spent in the store at each customer visit C. The 4,500 customer visits recorded
B
A skewed left shape means that the peak of the histogram is on the left side of the histogram. A skewed right shape means that the peak of the histogram is on the right side of the histogram. A. True B. False
B
At a birthday party, teams are chosen by putting everyone's name in a hat. Then names are drawn to make up each team. Is this sampling with replacement? A. True B. False
B
Does the average deviation always equal zero for every data set? A. Yes, because the deviations cluster about the mean B. Yes, because the positive and negative deviation cancel each other C. No, because this is not true D. No, because the average deviation equals zero for some data sets, but not for all datasets.
B
How is the sum of squares (SS) standardized into variance (σ2)? A. Divide by the number of data values B. Divide by the degrees of freedom C. Take the square-root of the sum of squares D. Sum of squares is the same value as the variance
B
In a data set used in statistics (imagine a MS Excel spreadsheet), information about the individuals are contained in the columns. A. True B. False
B
In a histogram for continuous data, what characteristic is shown on the x-axis, and what characteristics is shown on the y-axis? A. Bins of the data values, and bins of the frequency of the data values. B. Bins of the data values on the x-axis, and the frequency of the data values in the bins on the y-axis C. The frequency of the data values, and the data values in the data set. D. The data values in the data set, and the frequency of the data values
B
In a histogram for discrete data, what characteristic is shown on the x-axis, and what characteristic is shown on the y-axis? A. The frequency of the data values, and the data values in the data set B. The data values in the data set on the x-axis, and the frequency of the data values on the y-axis C. Bins of the data values, and the frequency of the data values D. Bins of the data values, and bins of the frequency of the data values
B
Match each characteristic of a distribution with the appropriate statistic for qualitative data. Location A. Number of categories B. Mode C. Bar chart
B
Match the appropriate set of statistics to the descriptions below. Extract the most information from a column of data A. Resistant statistics B. Efficient statistics
B
Match the appropriate statistic for a distribution of efficient statistics. Location A. Histogram B. Mean C. Standard deviation
B
Match the appropriate statistic for a distribution of resistant statistics. Spread A. Boxplot B. Inter-quartile range C. Median
B
Match the following statistics with the characteristic of a column of data that they summarize. Mean or median A. Spread B. Location C. Size
B
Match the two meanings below with their appropriate column titles in a frequency table. Proportion of the data values in a category A. Frequency B. Relative frequency
B
Percentiles (or quartiles) must always be a data value in the data set. A. True B. False
B
Percentiles are NOT positional statistics. A. True B. False
B
Randomly choosing several friends to go with you on an automobile trip would be what type of sampling situation? A. Random sampling of your friends with replacement B. Random sampling of your friends without replacement C. Random sampling of your friends with bias D. Random sampling of your friends with a guarantee of a representative sample
B
Skewness in a histogram is a property of what in the histogram? A. The number of peaks B. The tails C. The extreme values D. The peak
B
Statistics is the science of decision making using random selection of choices. A. True B. False
B
The distribution of a column of data is given by its shape, location, and symmetry. A. True B. False
B
The efficient measure of spread for a column of data is the? A. Average deviation B. Standard deviation C. Middle deviation D. The average of all the deviation in the data set
B
The mean (µ) is NOT needed to calculate a deviation. A. True B. False
B
The science of statistics summarizes information in a column of data with graphs, numbers, and computer outputs. A. True B. False
B
The value of the third quartile (Q3) can be less than the value of the first quartile (Q1). A. True B. False
B
To calculate variance, statistics does not average the deviations, instead it average the? A. The positive and negative deviations separately B. Squared deviations C. The square-root of the squared deviations D. The absolute value of the deviations
B
What characteristic is summarized by the width of the data values on a real number line? A. Shape B. Spread C. Location
B
What information about a data value is given by its deviation? A. The statistical distance and direction from the mean. B. The mathematical distance and direction from the mean C. The magnitude (absolute value) of the difference between the data value and the median D. How different the data value is from the mean and median
B
What information is extracted from a column of data by graphs? A. Precise values for the shape, location, and spread of a column of data values B. General trend of the data values as well as any major exceptions C. The size and the degrees of freedom of a column of data values D. The value of the mean and standard deviation for a column of data values
B
What is the general name for statistics that give information about a column of data? A. Inferential statistics B. Descriptive statistics C. Efficient statistics D. Resistant statistics
B
Which of the following answers is NOT one of our overall shapes? A. A uniform shape B. A modeless shape C. A symmetric shape D. A skewed shape
B
A data value less than the mean has a? A. Positive deviation B. Left deviation C. Negative deviation D. None of the above
C
How is a gap distinguished from an extreme value? A. A gap is close to the peak. An extreme value is far from the peak B. A gap is narrow, an extreme value is wide C. A gap fits as part of the overall shape. An extreme value is outside the overall shape D. There can be only one gap, while there can be many extreme values
C
In a boxplot of continuous data, what percent of the data values lie inside the box, and what percent of the data values lie outside the box? A. 75% and 25% B. 25% and 25% C. 50% and 50% D. 100% and 0%
C
In statistics, the statistical distance between two numbers is defined as A. Taking the difference between the two numbers B. Sum the two numbers, then divide by 2 C. Taking the difference between the two numbers, then dividing by the spread of the data D. The distance between the two numbers on a real number line found by using a ruler
C
Is the average deviation better than the standard deviation (σ)? A. No, because the standard deviation is a standardized version of the average deviation. B. Yes, because the average is the most representative value C. No, because the average deviation always equals zero D. Yes, because the average deviation is much quicker to calculate and much easier to use
C
Match each characteristic of a distribution with the appropriate statistic for qualitative data. Shape A. Number of categories B. Mode C. Bar chart
C
Match the appropriate statistic for a distribution of efficient statistics. Spread A. Histogram B. Mean C. Standard deviation
C
Match the appropriate statistic for a distribution of resistant statistics. Location A. Boxplot B. Inter-quartile range C. Median
C
Match the following statistics with the characteristic of a column of data that they summarize. Number of data values. A. Spread B. Location C. Size
C
The sum of squares (SS) is what type of measure of spread? A. A standardized measure of spread B. A normalized measure of spread C. A raw measure of spread D. An adjusted measure of spread
C
What characteristic is summarized by the middle of the data values on a real number line? A. Shape B. Spread C. Location
C
What is the appropriate denotation for variance? A. φ¯ for population, v¯ for sample B. μ2 for population, s2 for sample C. σ2 for population, s2 for sample D. VAR for population, var for sample
C
What is the general name for statistics that extract the most information from a column of data? A. Descriptive statistics B. Inferential statistics C. Efficient statistics D. Resistant statistics
C
What is the true and final, purpose of statistics? A. To find probabilities from probabilistic data B. To extract information out of columns of data C. To get information from data to help make better decisions D. To use mathematics to improve what we know
C
What makes resistant statistics work? A. They weight the data values lower when far from the mean B. They remove the high and low data values to eliminate any extreme values C. They look at the position of the data values, and not at their values D. The data values are divided by their deviation
C
What type of graph is most appropriate to use to display the shape of discrete data? A. A bar chart where the bars do not touch each other B. A pie chart where the slices of the pie touch one each other C. A histogram where the bars do touch each another D. A mathematical curve such as a bell-shaped curve
C
Why look at a chart to get shape information instead of looking at the data values themselves? A. This statement is false, it is always better to look at the data values directly to get shape information B. Statistical computer output will give charts, but not the column of data C. A chart is needed to summarize the shape characteristic so that we can see it D. Charts are much easier to look at than columns of data
C
What is the 40th percentile (P40) in the following ranked set of data (n=15)? 9, 13, 14, 14, 15 18, 19, 24, 30, 37 40, 41, 44, 44, 193
18.5
A Pareto chart is just a bar chart with the bars rearranged from the highest bar to the lowest bar. A. True B. False
A
A bigger standard deviation for a data set means the data values are? A. Spread wider apart B. Spread narrower together C. Spread more evenly about the mean D. Have a more symmetrical spread
A
A boxplot shows location and spread information as does a histogram. A. True B. False
A
A distribution of a column of data refers to what three characteristics of the column of data? A. The shape, location, and spread of the column of data B. The count, number of values, and the range of the column of data C. The pattern, peak, and ends of the columns of data D. The first mathematical moment, the second mathematical moment, and the sum of the column of data
A
A shoe store wants to know how much money, on average, their customers spend each visit to the store. Using their store records, they draw a sample of 4.500 customer visits and record the amount spent at each customer visit. The average of this data is calculated to answer the shoe store's question. What is the population in this sample? A. All shoe store customer visits B. The amount spent in the store at each customer visit C. The 4.500 customer visits recorded
A
Always look at your data first, before looking at your statistics. A. True B. False
A
At a local seminar, every attendee's name was put into a jar to win a small gift. Names were selected at random, then returned to the jar. This allowed the possibility of an attendee winning more than one gift. Is this sampling with replacement? A. True B. False
A
Two data sets have the same size, but Data set A has a sum of squares of 97 and Data set B has a sum of squares of 197. In which data set are the data values more widely spread out? A. Data set B, because 197 can have more variation than 97 B. Data set A, because a sum of squares 97 is smaller than a sum of squares of 197 C. Data set A, because 97 is closer to zero than 197 D. Data set B, because a sum of squares of 197 is bigger than a sum of squares of 97
D
Variance (σ2) is what type of measure of spread? A. A raw measure of spread B. A measure of spread normalized for shape C. A measure of spread adjusted for bias D. A measure of spread standardized for the number of data values
D
What are resistant statistics resistant to? A. Any possible bias in the data values B. The presence of gaps in the shape C. Any minor recording errors in the data set D. The presence of extreme values
D
What is the appropriate denotation for standard deviation? A. s population, σ for sample B. σ for population, std for sample C. µ for population, s for sample D. σ for population, s for sample
D
What is the formula for the sum of squares (SS)? A. Sum of squares = (x - xbar)^2 B. Sum of squares = (x - xbar) C. Sum of squares = ∑(x)2 − ∑(xbar)2 D. Sum of squares = ∑(x − xbar)^2
D
What is the general approach to analyzing the information in a histogram? A. First look at the modality, then look at the symmetry B. First look at the peak of the histogram, then look at the tails. C. First look for the mean, then look for the standard deviation D. First look at the overall shape, then look for exceptions.
D
What is the general name for statistics that are less affected by extreme values in a column of data? A. Inferential statistics B. Efficient statistics C. Descriptive statistics D. Resistant statistics
D
What type of graph is most appropriate to use to display the shape of qualitative data? A. A histogram where the bars do touch each another B. A bar chart where the bars do touch each other C. A pie chart where the slices of the pie touch one each other D. A bar chart where the bars do not touch each other
D
When denoting a percentile (Pk) what does the k stand for? A. The percentage of data values greater than (to the right of) the percentile B. That the data set has been ranked for lowest to highest C. This is archaic nomenclature, now k is no longer used D. Which percentile is desired, the 0th percentile up through the 100th percentile
D
Which of the answers below are NOT one of the steps to find any percentile (Pk)? A. Step 3: Find the Value of the percentile from the ranked data set B. Step 1: Calculate the Index C. Step 2: Move to the correct Position D. None of the other choices
D
Which of the following answers is NOT one of the first three columns in a frequency table? A. Category B. Relative frequency C. Frequency D. Cumulative frequency
D
Which one of the following answers is NOT correct about standard deviation? A. Standard deviation = √σ2 B. Standard deviation = √Variance C. Standard deviation ^2 = Variance- D. Standard deviation = Variance^2
D
Why do positional statistics work for a data set containing extreme values? A. Because positional statistics are not a very sensitive type of statistics B. Because extreme values occur near the mean where the positions of the data values are close together C. Because the range of position is (0, n), but the range of the values is (-∞, ∞). D. Because in the tails, a big change in value is usually a small change in position
D
Why is it important to look at the shape of a column of data before interpreting any statistics? A. Because shape determines the location and the spread of the column of data B. To see that all data values were included in the statistical analysis C. Because graphs for shape come first in the computer output D. To see if the data is unimodal, symmetrical, and without any exceptions
D
The mean (µ) is used when thinking about the data values in a column of data because? (select two of the answers below) A. The mean is easier to calculate than the median B. The mean can be used in the advanced statistical methods C. A single number is easy to think about D. The mean best represents the values in the column of data
idk lol
