chapter one and two test

how do you calculate the z score?

(x-mean)/standard deviation

What is the difference between class limits and class boundaries? Why do we organize raw data into frequency distributions and then display the results in graphs like a histogram?

Class limits have gaps between the upper limit of a class and the lower limit of the class that follows it, the class boundaries do not have the gaps. We organize raw data and graph it because we want to understand how the data is distributed on the number line. ___________

What is the difference between a relative frequency table and relative frequency distribution?

Frequency tables are for qualitative data. Frequency distributions are for quantitative data.

The NHTSA (National Highway Traffic Safety Administration) conducted a study of accidents involving motorcycles. The data included the ages of motorcyclists involved in accidents. If the researchers want to describe the typical age of a motorcyclist involved in a crash, which measure of the center is likely most appropriate? A. Mean B. Median C. Mode D. Range E. Mean Absolute Deviation

Mean

.Each patient undergoing an annual checkup at a physician's office in Canada is weighed. The weights are recorded for each patient in kilograms (kg). What unit of measurement would the standard deviation and variance of these weights have respectively

A. kg and kg²

In your own words describe what a measure of variation (dispersion) reveals about a data set.

Measures of dispersion indicate the spread in the data points. You might also say that measures of dispersion indicate the degree to which the data points are clustered together

Is the following an example of a statistic or a parameter? Only 4% of students who applied to Harvard were admitted

Parameter

what is the difference between qualitative and quantitative data?

Quantitative data is numeric in nature. Qualitative data is not numeric.__

If the population mean for a measurement is 98.3 and the population median for the same measurement is 92.6, the population is most likely: Left-skewed, Right-Skewed, or Symmetric?

Right skewed

In a right-skewed distribution, the median is 16.2. Which of the following values could be the mean for the distribution? (select all that apply) A. 12.3 B. 17.8 C. 15.4 D. 18.1 E. 16.2 F. 13.4

Right skewed meaning mean is larger than median answers: 17.8,18.1,

The empirical rule assumes the shape of the distribution is known. What shape is assumed? It is given different names:

bell-shaped, mound shaped and symmetric, or normal._______________________________

Civil engineering graduate students weighed a random sample of vehicles passing over a small bridge here in Miami. The standard deviation for the weights of the sampled cars was 953 pounds. What unit of measurement would the variance of the data have? A. Pounds B. Root Pounds C. Pounds Squared D. Kilograms

c pounds squared ( S^2)

when it is measurement data is it discrete or continuous

continuous

when using a ruler, speedometer or scale is this measurement discrete or continuous

continuous

The university tabulates and stores students' cumulative GPAs. This set of GPAs is an example of: (select all that apply) A. continuous data B. discrete data C. qualitative data D. ordinal level data E. quantitative data

continuous and quantitative

The heights of the athletes playing on the men's basketball team are recorded each year. This set of measurements is an example of: (select all that apply) A. continuous data B. discrete data C. qualitative data D. ordinal level data E. quantitative data

continuous and quantitative data

9.The number of friends each Facebook user has is an example of: (select all that apply) A. continuous data B. discrete data C. qualitative data D. nominal level data E. quantitative data

discrete and quantitative data

. Does the following data set contain continuous data, discrete data, or qualitative data? Engineers count and record the number of cars that run a red light at the intersection of 8th and 107th streets in Miami over the course of three days of observations.

discrete data

how do you calculate relative frequency?

divide the frequency by the amount of the data and multiply by 100 to get the percent

Which of the following are properties of the arithmetic mean? (select all that apply A. Every data value is included in the calculation of the arithmetic mean. B. The sum of the deviations from the mean is always zero. In other words, . C. The arithmetic mean is robust, which means that it is not heavily influenced by extreme values. D. The mean is the "center of mass" or centroid of the data set.

every data set is included in the calculation of the arithmetic mean , the sum of deviation from the mean is always zero, the mean is the center of mass or centroid of the data set

why do researchers relay on sample data instead of the full population of data?

it can be to expensive or difficult to conduct a census,impossible in some cases to take all the measurements

when it is count data is it discrete or continuous

it is discrete

If the population mean for a measurement is 12.4 and the population median for the same measurement is 15.8, the population is most likely: Left-skewed, Right-Skewed, or Symmetric?

left skewed

Final exam scores for STA3123 have an average of 68.3. The median score is 72, and the most common score (the mode) for the class is 75. Is the distribution likely left skewed, right skewed, or symmetric?

left skewed the mean is less than the mode and median

Among the three measures of the center we studied (mean, median, and mode), which is generally preferred?

mean

what is the order of left skewed distributions

mean, median, and mode

.A women's volleyball coach would like to report the typical height of athletes that compete in her sport. Which measure of the center would be the best choice in this situation? A. Median B. Mean C. Mode D. None of the above

mean,(Since human height has physical limitations, it is unlikely to have extreme values that will unduly influence the mean.)

What is the mean?

measures the center

Some writers earn very large annual salaries, but this sort of financial success is unusual. What measure of the center would you recommend to describe the typical earnings for writers?

median

The NHTSA (National Highway Traffic Safety Administration) conducted a study of accidents involving motorcycles. The study included observations of helmet color. If the researchers want to describe the typical color of helmet involved in a motorcycle crash, which measure of the center is most appropriate? A. Mean B. Median C. Mode D. Range (this is not a measure of the center) E. Mean Absolute Deviation (this is not a measure of the center)

mode

what is the order for right skewed distributions

mode median mean

In a right-skewed distribution the order of the mean, median, and mode on the number line from left to right is: A. Mean, Mode, Median B. Median, Mean, Mode C. Mode, Mean, Median D. Mode, Median, Mean

mode, median, mean *refer back to the graphs in notes*

What is a parameter?

or A numerical summary of a population. Like a mean, median, range... of a population

In July 2011, 89.6% of all Florida International University Law School graduates passed the bar exam, which incidentally was the best passage rate in Florida. Is this passage rate an example of a population parameter or a sample statistic?

parameter

7. An online retailer reviewed all of its sales and found that the average checkout total was $54.13. The average ($54.13) is an example of a statistic or a parameter? Why

parameter? Why? because it came from all of the data.

when we think of parameter you should associate this with

population

what is the difference between population parameter and sample staristic set?

population parameter is derived from the full set of the population while a statistic is derived from a sample set

5. Airlines weigh and record the weight of each piece of checked luggage that flies on their aircraft. This set of values is an example of: (select all that apply)

quantitative data,A. continuous data

what is discrete numerical data

result when the number of possible values is either a finite number or a countable number

when we think of the word statistic we should think of

sample

what is the number range that is acceptable for using range

should not go more than 7

A sample of law students attending the evening program is selected from FIU and their average age in years is 28.7. Is this average age an example of a population parameter or a sample statistic?

statistic

i am interested in the average fine issued for speeding tickets in Miami. I reviewed a sample of the tickets issued. The average I calculated from the sample of data is an example of a statistic or a parameter? Why?

statistic because they reviewed a sample

Is the following an example of a statistic or parameter? On the day of the final last year, I asked every third person who entered the classroom how many hours he/she studied for the exam. The median response was 8.5 hours.

statistic: every third person

If the population mean for a measurement is 76 and the population median for the same measurement is 76, the population is most likely: Left-skewed, Right-Skewed, or Symmetric?

symmetric

Left-skewed distribution means LESS than what... think of L L

the mean is less than the median. Left Mean ( smaller mean) (Less Left)

for left skewed distribution graph fill in the blank question we should know that

the tail mean is towards the left

for the right skewed graph fill in the blanks you should know the graph is

the tail of the mean is towards the right side (the graphs are opposite from their names such as right skewed being towards the left)

what type of problem is this and how do we solve it? The average weight of cars on U.S. roads is 4,009 pounds. If we assume the standard deviation for the weights of the cars is 919 pounds, create an interval that would capture the weights of at least 88.9% of all cars on U.S. roads.

this is an empirical step one: realize that 95% on the chart is 2( from the notes ) step 2: plug into the equation to find intervals (mean-k(standard deviation, mean + k(standard devation) = 25-2(4.2), 25+2(4.2) should get 16.6, 33.4+step 4 check work 25-8.4 will give you 16.6 and 25+ 8.4 will give you 33.4 so your answer should be 16.6min-33.4 min due to them askign at least

how would you solve this problem? and what type of problem is it?

this problem is a empirical type problem, (safe to assume these heights are normally disturbed) . first step: find the z score for 60.6inches tall ( 60.6-58.7/1.9) you cant stop there because they want to know 54.9-60.6 not just 60.6-58.7 witch will give you 68%. you will need to dived the 68% by two to get just on proportion of 54.9-60.6 so like (58.7 of the bell shape curve) at this point you should have 34. you will do the same egact thing for 54.9-58.79 (54.9-58.7/1.9) (ans/2). after finding the two add them together and you should receive your answer.

13.True or false: a measurement's z score provides us with the number of standard deviations the measurement is away from the mean for the set of measurements

true

True or False: Continuous data consists of numerical measurements that fall along a continuous scale without gaps or spaces between any two achievable values?

true

True or False: In a bell curve, the mean, median, and mode are all in the same place

true

True or false: When creating a histogram with a very large amount of data, it is possible to use more classes than when creating a histogram for a relatively small amount of data. Also, a histogram created from a large data set that has been organized into many classes will tend to appear like an almost smooth curve.

true

when is the median prefered

when extreme values are present

what are some examples of qualitative data

year in school, live in or off campus, major, and gender

What is a census?

an official count or survey of a population, typically recording various details of individuals.

What is qunatitative data?

are measurements that are recorded on a naturally occurring numerical scale

what is a class frequency

is the number of observations belonging to the class

What is a population?

is the set of all measurements interest to the investigator

True or false: The empirical rule can be used to determine the minimum percentage of data contained in an interval of the form ( mean- k slandered deviation , mean + stranded deviation k ) where k is greater than 1.

. This describes Chebyshev's rule, true

how do you convert a set if given class limits into a suitable set of class boundaries ?

1. take the 2nd lower class level and subtract it by the 1st higher class level. 2. take the number found in step one and dived that by 2 . 3. add that given answer from step two back to the upper fist level class to get your 1st upper higher class boundary. if too confusing refer back to class notes

In a left-skewed distribution, the median is 64. Which of the following values could be the mean for the distribution? (select all that apply) A. 62.1 B. 61.3 C. 65.4 D. 67.0 E. 64.2 F. 62.9

62.1 61.3 62.9 remember the mean is less in a left skewed

A. According to the empirical rule, approximately what percent of data is captured between mean- 2 deviation and mean + 2 devation ?

95%

what is a class

A class is one of the categories into which data can be classified

At the World Cup a statistician keeps track of the time when every first goal in a match is scored. The statistician reported that the mean time it takes for a goal to be scored is 35.3 minutes. Suppose that the statistician indicated that the time-to-first-goal distribution was skewed to the right. Which of the following values is most likely the value of the median time-to-first-goal? VS A. 44.6 C. 38.1 B. 32.5 D. 35. 9

B. 32.5 ( mean is more in Right skewed its not L-ESS FOR Left)

Airlines count and record the number of passengers on each flight they operate. This set of values is an example of: (select all that apply)

B. discrete data E. quantitative data

1. Some barbers, hairdressers, and cosmetologists earn very large annual salaries due to celebrity clients, product lines, and/or very successful salons. However, workers in the industry do not typically earn such large salaries. If you worked for the Bureau of Labor Statistics, what measure of the center would you recommend to describe the typical earning for barbers, hairdressers, and cosmetologists? A. Mean B. Median C. Mode D. Range (this is not a measure of the center) E. Mean Absolute Deviation (this is not a measure of the center)

C. median

The university collects and stores students' overall ratings of professors. The ratings fall on a scale that range from excellent to poor. This set of ratings is an example of: (select all that apply) . continuous data B. discrete data C. qualitative data D. ratio level data E. quantitative data

C. qualitative data

The empirical rule provides us with the approximate percent of data within some given interval. What does Chebyshev's theorem give us?

Chebyshev's theorem gives us a lower bound for the amount of data that can be found in an interval that is symmetric with respect to the mean._

What is class width?

The difference between the upper and lower class boundaries

What useful information can Chebyshev's theorem provide us with for a set of data? What assumptions about the shape of the distribution of the data does the theorem make?

The theorem tells us the minimum percentage of data located within a given interval that is symmetric around the mean of the set of data. Chebyshev's theorem does not make any assumptions about the shape of the data set

In a left-skewed distribution, is the value of the mean larger or smaller than the median? What about in a right-skewed distribution?

The mean is less than the median in a left-skewed distribution. The mean is greater than the median in a right-skewed distribution.

The median is sometimes referred to as a robust measure of the center. What is meant by this and explain how this quality of robustness is both a strength and a weakness

The median is more resistant to the effect of extreme values than the mean. That is useful when you want to describe the center of a data set that has extreme values on one end of the distribution; however, the same quality in general is a weakness because the median is insensitive to differences between data sets that just happen to have the same middle number.__

why is the median and mode the not preferred method to use for measurement of the center

The median should be used when extreme values might make the mean unrepresentative of what is typical in the data set. The mode is best for data that is qualitative.

Why is the standard deviation generally preferred to the variance as a measure of dispersion (variation)?

Two possible reasons: the units of the standard deviation are the same as the units of the original measurements, and Chebyshev's theorem and the empirical rule help us to use the standard deviation to know something important about the distribution of data sets.

. NPR (National Public Radio) claims that their average listener listens to NPR programming for 3.2 hours every day. To test this claim a newspaper conducted a poll of 200 random NPR listeners. Each of the polled listeners were asked to estimate the amount of time they listened to NPR each day. The results of the poll were summarized and expressed as a z score by using the claimed value of 3.2 hours as the population mean. The resulting z score was -0.46. Based on the z score, does NPR's claim appear to be plausible?

Yes, because -0.46 is not extreme or unusual. Usually, if the claimed mean is correct, the sample mean will be very close to the claimed mean value. This in turn will produce a z score that is typically small in absolute value (i.e., |z| is between 0 and 1.2).

According to a report by Common Sense Media, teens are spending an average of 9 hours per day in front of a screen for entertainment. The standard deviation for the time teens spend in front of a screen for entertainment is 2.2 hours. Would it be unusual for a teen to spend 2 hours or less in front of a screen for entertainment each day? Why or why not? (Hint: use the z-score to support your answer.) Y

Yes, because the z score for these times would be less than or equal to -3.18.

6. A manufacturer that makes microprocessors for cellular phones randomly selects four microprocessors from their production line in order to test them. These tests are done to determine the length of time the microprocessors function under extreme use. The manufacturer would like to calculate some measure of dispersion (variation) for the measurements taken from each sample of four microprocessors selected. Would the range be an acceptable option under these circumstances? Why or why not?

Yes, because there are only four measurements in the set of collected data.

what is continuous numerical data?

a result from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps. Example: The finishing times of a marathon

What is a sample?

a subset of measurements selected from the population . A subset of a population, often taken to make inferences about the population. We calculate statistics from samples.

examples of quantitative data

age, gpa, salary, cost of books

8. True or false: Chebyshev's theorem can only be used with normally distributed

false The theorem can be used for any distribution

The relative frequency for a class is defined as the class frequency divided by the sum of the

frequencies

how do you calculate relative frequency?

frequency/# of observations. in other words Count the number of times each item appears in your data. example: question 17 from lab, classes 7-11 how many numbers are in that set ? would be 7 ( 7,8,9,9,10,11,11)

what is a statistic?

is a numerical measurement describing some characteristic of a sample drawn from the population