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