Statistics test 1
What is the goal of learning statistics?
To learn to distinguish between statistical conclusions that are likely to be valid and those that are seriously flawed
True or false? A histogram and a relative frequency histogram, constructed from the same data, always have the same basic shape.
True. A relative frequency histogram will have a different scale on the y-axis but the same shape as a regular histogram.
Which of the following is NOT a property of the standard deviation?
When comparing variation in samples with very different means, it is good practice to compare the two sample standard deviations.
Which of the following is NOT a measure of center?
census
Q2 is also known as
median
the bars in histograms
touch
The square of the standard deviation is called the _______.
vairance
can qualitative variables have values that are numeric? why or why not
yes, it is possible to have numeric values that do not measure anything which makes them qualitative rather than quantitative
Which measure of center must be equal to an actual data value? Explain why.
Since the mode is the most frequent observation that occurs in the data set, it must be an actual value from the data set.
Describe the sample standard deviation in words rather than with a formula.
The sample standard deviation is the square root of the quotient of the sum of the squared deviations from the mean and (n-1).
Which of the following is NOT a value in the 5-number summary? Mean, Q1, Median, Minimum
mean
A value at the center or middle of a data set is a(n) _______.
measure of center
The measure of center that is the value that occurs with the greatest frequency is the _______.
mode
Which distribution shape (skewed left, skewed right, or symmetric) is most likely to result in the mean being substantially smaller than the median?
A distribution that is skewed left will likely have a mean that is smaller than the median since the extreme values in the tail tend to pull the mean to the left. Your answer is correct.
After constructing any relative frequency distribution what should be the sum of the relative frequencies?
1 or 100%
For any set of data, at least _______ of the data will be within two standard deviations of the mean. For a bell-shaped distribution, approximately _______ of the data will be within two standard deviations of the mean.
3/4 95%
For any set of data, at least _______ of the data will be within three standard deviations of the mean. For a bell-shaped distribution, approximately _______ of the data will be within three standard deviations of the mean.
8/9 99.7%
If two data sets use different units of measure, which should you calculate to compare the variability of the two sets of data?
Coefficient of variation
Suppose the list below shows how many text messages Elyse sent each day for the last 10 days. If Elyse wants to know how many text messages she typically sends each day, which measure of central tendency better describes the typical number of text messages per day? 21 22 24 26 26 29 32 32 33 88
Median; The median of 27.5 is a better representative of the center since it is resistant to the one extreme value. The mean of 33.3 is not representative of the typical number of texts since only one number is larger than the mean.
Which of the following is associated with a parameter?
Data that were obtained from an entire population.
If a professor adds 10 points to each student's final exam score, how will it affect the distribution of final exam scores?
The center will change, but the shape and spread will remain the same.
Which level of measurement consists of categories only where data cannot be arranged in an ordering scheme?
nominal
In a graph, if one or both axes begin at some value other than zero, the differences are exaggerated. This bad graphing method is known as _______.
nonzero exists
A(n) _______ distribution has a "bell" shape.
normal
_______ are sample values that lie very far away from the majority of the other sample values.
outliers
the _________ is the entire group of individuals or items being studied
population
Which measure of variation is most sensitive to extreme values?
range
A _______ histogram has the same shape and horizontal scale as a histogram, but the vertical scale is marked with relative frequencies instead of actual frequencies.
relative frequency
In a _______ distribution, the frequency of a class is replaced with a proportion or percent.
relative frequency distribution
Suppose every student in a class is surveyed. It is reported that 75% of the class plans to take another math class. What kind of statistics is this and why
Descriptive, the results of the class sample are described without making any generalizations about the population of the school
Which of the following is typically the least important factor to consider when conducting a statistical analysis of data
Formula calculation
Why does the formula for calculating the sample variance , involve squaring the difference between each value and the mean?
If the differences were not squared, then the sum of all deviations from the mean would always be zero since the positive deviations are balanced by the negative deviations.
Why does the formula for calculating the sample variance, involve division by n-1 instead of n?
If the formula involved division by n, the sample variance would be biased and consistently underestimate the population variance.
Which of the following would be considered practically significant?
In a very large study, it was found that Treatment I resulted in 93% success while Treatment II resulted in 75% success.
Every student in the class is surveyed and it is found that 75% of the class plans to take another math class. It is reported that 75% of all students at the school plan to take another math class. What kind of statistics is this and why
Inferential, the results of the class are extended to make a generalization about the population of all the students
Which of the following consists of discrete data?
Number of suitcases on a plane
Which of the following is NOT a level of measurement?
Quantitative
Which of the following is NOT a voluntary response sample?
Quiz scores from a college level stats course are analyzed to determine student progress
Suppose you want to know if more technical service calls are made to homes with cable television or with satellite dish television. Should you use frequencies or relative frequencies to make the comparison? Why?
Relative frequencies should be used since there is likely a difference in the number of users of cable and satellite television. If you make comparisons using frequencies, the results can be very misleading for different population sizes.
The Range Rule of Thumb roughly estimates the standard deviation of a data set as _______.
S= range/4
A collection of data on class sizes at a community college produces the five-number summary below. Comment on the shape of the distribution of class sizes. Min=12 Q1=22 Q2=35 Q3=38 Max=40
The distribution appears to be skewed left since the median is further from the first quartile than the third quartile. Also, the left whisker would be longer than the right whisker in a boxplot for the data.
The following five-number summary represents the annual snowfall totals for a Midwest town for the last 75 years. Comment on the shape of the distribution of snowfall totals. Min= 14 Q1=17 Q2=21 Q3=29 Max=38
The distribution appears to be skewed right since the median is closer to the first quartile than the third quartile. Also, the right whisker tends to be longer than the left whisker in a boxplot of a right-skewed distribution.
What does it mean for the findings of a statistical analysis of data to be statistically significant?
The likelihood of getting these results by chance is very small.
Which measure of center (mean or median) is resistant? Explain what it means for that measure to be resistant.
The median is resistant because it is not sensitive to extreme values in the data set. If the largest observation was doubled, for example, the median would not change since that largest value does not factor into its computation.
Describe the sample variance in words rather than with a formula.
The sample variance is the sum of the squared deviations from the mean, divided by (n-1).
If someone's gross annual income has a z-score of positive 2, what can be concluded?
Their income is 2 standard deviations above the mean income.
Suppose you want to calculate the z-score for your height. How will the z-scores compare if you use your height in inches verses centimeters?
The z-scores will be the same regardless of the unit used for your height because z-scores are unitless
Methods used that summarize or describe characteristics of data are called _______ statistics.
descriptive
what must be true for a sample to be a random sample?
every member (or sample) must have the same chance of being selected as every other member
What is true about random and simple random samples
every simple random sample is also a random sample
The heights of the bars of a histogram correspond to _______ values.
frequency
A _______ helps us understand the nature of the distribution of a data set.
frequency distribution
We utilize statistical _______ to look for features that reveal some useful or interesting characteristics of the data set.
graphs
Which of the following would be classified as categorical data?
hair color
the _______ is the subset of the population that is being studied
sample
A _______ is a plot of paired data (x,y) and is helpful in determining whether there is a relationship between the two variables.
scatterplot
A histogram aids in analyzing the _______ of the data.
shape of distribution
A data value is considered _______ if its z-score is less than minus2 or greater than 2.
significantly low or significantly high
Why is it important to learn about bad graphs?
so that we can critically analyze a graph to determine whether it is misleading
Class width is found by _______.
subtracting a lower class limit from the next consecutive lower class limit
Whenever a data value is less than the mean, _______.
the corresponding z-score is negative
For data sets having a distribution that is approximately bell-shaped, _______ states that about 68% of all data values fall within one standard deviation from the mean.
the empirical rule
Which of the following is NOT a characteristic of the mean?
the mean is called the avg by statistics
Which characteristic of data is a measure of the amount that the data values vary?
variation
When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the mean, we call the new value a _______.
z-score
