Math 250 Unit 1

give an example of a small data set with a mean of 75 with a relatively small standard deviation. State the mean and standard deviation for your set.

-measure of average deviations that the various data values fall from the mean. Data set varies: 73,74,75,76,77 mean:75 STD: 1.825741858 Deveation is very small

Q3

75th percentile =quartile.inc ( , 3)

Identify the data level (nominal, ordinal, interval, or ratio) that best describes each of the following cases: The temperature in Paris, France at noon

= Interval

Observational Studies

Observational data comes about by measuring what is. Virtually all of the data we routinely encounter are observational. Census data are observational, they are a measure of how things are in a specific geographic area at a given point in time. Example: If you are trading stock, the market data you receive are observational.

Empirical Rule:

One sigma rule: If the distribution of the data is bell-shaped, then About 68% of the data should lie within 1 standard deviation of the mean. Two sigma rule: About 95% of the data should lie within 2 standard deviations of the mean. Three sigma rule: About 99.7% of the data should lie within 3 standard deviations of the mean.

Classify each of the following as to the level of measurement (nominal, ordinal, interval, or ratio). your T-shirt size (S, M, L, XL)

Ordinal

Identify the data level (nominal, ordinal, interval, or ratio) that best describes each of the following cases: Client satisfaction survey responses: Poor, Average, Good, and Excellent.

Ordinal level

Classify the resulting: Qualitative or Quantitative. discrete or as continuous. & Nomina, Interval, Ratio or Ordinal: Toss a Coin and Record head =1 and tail =2

Qual, Neither, Nominal

Classify each of the following as qualitative (categorical) variables or as quantitative variables. For those which are quantitative, further classify as either discrete or continuous Names of spices in your cupboard

Qualitative

In each of the following, classify the resulting data variable as qualitative or as quantitative. If quantitative, label as discrete or as continuous. Manufacturer name of a randomly chosen door from an international air port

Qualitative

Classify the resulting: Qualitative or Quantitative. discrete or as continuous. & Nomina, Interval, Ratio or Ordinal: Height of 4 randomly selected students

Quant, Continuous, Ratio

Ordinal Data:

Represents categories that have some associated order. Allows for ranking of the data values. Ex: Very good Very bad, Fair

The graph at the right is a bar graph of the distribution of hours spent playing video games over the past week from a collection of randomly selected teenagers in the United States. Answer the following: Determine the mean and the median length of time this group of selected teenage males spent gaming during the last week.

Step 1: Create a Frequency table to see all the data: Step 2: =Median (All Hrs) Step 3: =Mean((h*f) /frequency total) A rough estimate of the mean just by looking at the values would be 9 to 10 hours. The mean can can found from the associate frequency distribution which will measure 9.5829675. The median is the value that is halway mark when the hours and frequency are put in order on a chart, thus the median is 8 hours

Determine if there are any outliers based on the 1.5 IQR rule. Final classification of outliers, if any exists, must be stated explicitly.

Step 1: IQR = Q3-Q1 1.5*IQR step 2: Find lower limit Q1 - (1.5*IQR) step3: Find Upper Limit Q3+ (1.5*IQR) Step 4: Compare your upper and lower limit Ex: Min =0 Lower limit = 3.375 Is there a Outlier? Yes, min is lower than the lower limit.

The Gallup News Service conducted a survey of 1004 randomly selected adults 18 years and older, asking, "Do you have a great deal of concern regarding Global Warming?" Of the 1004 adults surveyed, 40% said they worried about Global Warming a great deal. The implied sample in this study is

The 1004 randomly selected adults aged 18 and older

Quantitative Data:

is measured on an interval or ratio scale. Ex: Performing arithmetics, Number of claimed tax dependents, number of fans

Q1

25th percentile =quartile.inc ( , 1)

After first assuming the data represents a population instead of a sample in problem #7, what is the z-score of the first piece of data listed (the data value 22)?

Step 1: Population Mean Ex: =AVERAGE(M62:Q65) Step 2: Population Standard Deviation Ex: =STDEV.P(M62:Q65) Step 3: Z Score: Ex: = (22- pop mean)/ St Devation Population. Note: 22 is given value that you plug in. The Z score for value of 22 in population data for this data set is approx. -0.14081913. This indicates that the value is very close but still below the mean.

Which score has a higher relative position: a score of 76.8 on a test for which xbar = 60.5 and s = 6.2 , or a score of 249.6 on a test for which xbar = 180.1 and s = 26.9? (Note: xbar represents the mean value of the sample of tests collected.)

zscore = Mean/st deviation Step1: Zscore 1 (76.8-60.5)/6.2 = 2.629 step 2: Zscore 2 (249.6-180.1)/26.9 = 2.583 The score of 76.8 has a higher relative postion than the score of 249.6 because the z score for the test score 76.8 is higher than the Z score of the test score 249.6. Although the difference is very small, its still lower

A recent national study about the effectiveness of Echinacea in cold treatments for adults was performed by a medical school in Texas. The results stated that 19.2% of the randomly chosen 722 adult subjects from across the U.S.A.that were placed in the placebo group noted that their treatment appeared to shorten the length of their colds. The descriptive statistic of interest in this study is_____________.

19.2% of the randomly chosen 722

Identify the data level (nominal, ordinal, interval, or ratio) that best describes each of the following cases: The title of a radomly selected individual's favorite book

= Nominal

Identify the data level (nominal, ordinal, interval, or ratio) that best describes each of the following cases: Placement (1st, 2nd, etc.) within a video game tournament

= Ordinal

Identify the data level (nominal, ordinal, interval, or ratio) that best describes each of the following cases: The height of a randomly selected semi tractor and trailer on I-70

= Ratio

Compute at the right in an adjacent Excel cell the value of the mathematical calculation shown. Then, give this value in a rounded two decimal place percent form (eg. 57.34%) 51-43/11.2

=(51-43)/11.2 Then on a new column =N50 <-- Whatever the answer was in past box, write the box name to get percent. 71.43%

A random sample of students was chosen. The table at the right shows the number of minutes each student worked out in a week. Give the standard deviation of the data.

=STDEV.S ( ) .s = sample Standard deviation

Calculate the variance:

=VAR.S ( ) For Sample =VAR.P( ) For population Units are squared! Ex: hr^2

Calculate the mean of the data.

=average ( )

Calculate the Average of the data in excel

=average( ) Ex: Then you want to divide the average by said data, Remember to put =B13/$E$16 The $ will allow the number to remain the same regardless.

Max

=max( )

Determine the range of the data.

=max( ) - min ( )

Determine the median of the data.

=median ( )

Median

=median ( ) 50ths Percentile

Min

=min ( )

Calculate the Percentile Rank Ex: Using Excel, determine the percentile rank for someone who worked 33 hours per week.

=percentile rank.inc( , ) Example: =percentilerank(B6:F65,33)

Calculate the 35th percentile:

=percentile.inc ( ,0.35)

What is the probability that a randomly selected person from this data list will travel at most 13 days?

Add Up the Relative Frequency up to 13 days 0.2+0.28 = 0.48 Want it in percent Answer: 48%

Inferential Statistics:

Aid in making decisions and predictions about populations and processes for which it is impractical to obtain measurements on each member. The object of inferential statistics is to make reasonable guesses about the population's characteristics using sample data.

The Gallup News Service conducted a survey of 1004 randomly selected adults 18 years and older, asking, "Do you have a great deal of concern regarding Global Warming?" Of the 1004 adults surveyed, 40% said they worried about Global Warming a great deal. The implied population in this research study is

All adults aged 18 and older

A recent national study about the effectiveness of Echinacea in cold treatments for adults was performed by a medical school in Texas. The results stated that 19.2% of the randomly chosen 722 adult subjects from across the U.S.A.that were placed in the placebo group noted that their treatment appeared to shorten the length of their colds. The implied population in this study is:

All adults in United States

A recent national study about the effectiveness of Echinacea in cold treatments for adults was performed by a medical school in Texas. The results stated that 19.2% of the randomly chosen 722 adult subjects from across the U.S.A.that were placed in the placebo group noted that their treatment appeared to shorten the length of their colds. The implied sample in this study is

All the randomly chosen adult subjects of the placebo group in the study

What are Population Parameters:

Are facts about the population. Since parameters are the description of a population, a population can have many parameters.

Construct an appropriate stem-and-leaf plot for the data given. Then, describe the shape of the distribution of the data set (either skewed left or skewed right or symmetric).

Creating a Stem and leaf plot: Stem = 0, 10, 20, 30 Leaf = The ending number Stem =1 mean 10 Leaf = 3 mean 10+3 = 13 total. The distribution seems to be skewed to the left as the tail end starts towards the smaller stem of values. See Stem and leaf plot on the right side.

Continuous Data:

Data that can take on any value within some interval Ex: Height, Temperature in Kelvin, time

Nominal Data:

Data that represents whether a variable possesses some characteristics. Nominal Scale are categorical ex: Sex, hair color, Toss a coin head=1, Tails =2,

The Gallup News Service conducted a survey of 1004 randomly selected adults 18 years and older, asking, "Do you have a great deal of concern regarding Global Warming?" Of the 1004 adults surveyed, 40% said they worried about Global Warming a great deal. The purpose of the data collection is to perform

Descriptive statistics

Double blind Studies:

Double blind studies are used to counter the placebo effects. In double blind studies the subjects are not told whether they are members of the treatment group or the control group. The evaluators (the persons that measure the response variable) are also not told whether their subjects are members of the control or experimental groups. Double blind studies are the gold standard in design of experiments for new drug therapies.

Scientific Method:

Gather info, Formulate a preliminary hypothesis,Collect data, if the data supports the hypothesis it becomes the law. If it doesn't create a new hypothesis.

What is the interquartile range of the shoe laces?

IQR = Q3-Q1 IQR = 75-50 = 25 mm

Interval Data:

If the data can be ordered and the arithmetic difference is meaningful. Ex: Temperature Interval data have an arbitrary zero value.

Discrete Data:

In which the observation are restricted to a set of values such as 1,2,3 that poses gaps is called discrete Ex: IQ scores in whole numbers, Numbers of diff color boxes of crayons

Classify each of the following as to the level of measurement (nominal, ordinal, interval, or ratio). the year of the last presidential election

Interval

Identify the data level (nominal, ordinal, interval, or ratio) that best describes each of the following cases: The temperature in randomly chosen room within a 5-star hotel

Interval

Identify the data level (nominal, ordinal, interval, or ratio) that best describes each of the following cases: The temperature (in degrees Fahrenheit) of patients with pneumonia.

Interval level

Descriptive Statistics:

Is Analyzing observed measurements usually from a sample. Descriptive methods describe and summarize data. Descriptive data is the collection, organization, analysis and presentation of data. The application of descriptive statistical tools is usually ad hoc, that is the exact method of analysis changes from one problem to the next. The importance of this as an informational producing tool related to the amount of data to be comprehending the data in its entirety is not difficult and descriptive statistical aids are of little value. Ex: Ca Test Crash, to find that airbags will release most of the time.

A Statistic:

Is a factor or characteristic about the sample.

What is a Sample:

Is a subset of the population which is used to gain insight about the population. Samples are used to represent a larger group, the population.

Is the distribution symmetric, uniform, skewed left, skewed right, or none of these?

It appears that the data is skewed to the left slightly as seen by the frequency classes near 9 to 12 hour interval of values.

Qualitative Data:

Measured on a nominal or ordinal Scale. Ex: Gender, occupation, Eye Color

Determine the median length of the laces.

Median length is 55mm. Represented by the middle line in the box.

Mutually Exclusive

Mutually Exclusive Probability Law 6: Union of Mutually Exclusive Events Two events are mutually exclusive if they have no outcomes in common. If the events A and B are mutually exclusive, then P(A∪B)=P(A)+P(B

Classify each of the following as to the level of measurement (nominal, ordinal, interval, or ratio). favorite M & M color

Nominal

Identify the data level (nominal, ordinal, interval, or ratio) that best describes each of the following cases: Answering "yes" or "no" on a survey question

Nominal

Identify the data level (nominal, ordinal, interval, or ratio) that best describes each of the following cases: The region of the U.S. in which an individual lives: North, South, East, or West.

Nominal level

The Gallup News Service conducted a survey of 1004 randomly selected adults 18 years and older, asking, "Do you have a great deal of concern regarding Global Warming?" Of the 1004 adults surveyed, 40% said they worried about Global Warming a great deal. The characteristic being measured is

Percentage of adults aged 18 and older who are greatly concerned about Global Warming

IQR

Q3-Q1

In each of the following, classify the resulting data variable as qualitative or as quantitative. If quantitative, label as discrete or as continuous. Manufacturer of a randomly chosen vehicle in a local store's parking lot

Qualitative

Classify the resulting: Qualitative or Quantitative. discrete or as continuous. & Nomina, Interval, Ratio or Ordinal: The amount of time each of the five basketball players play during a game

Quant, Continuous, Ratio

Classify the resulting: Qualitative or Quantitative. discrete or as continuous. & Nomina, Interval, Ratio or Ordinal: Weight of sugar imported by US each day for a year

Quant, Continuous, Ratio

Classify the resulting: Qualitative or Quantitative. discrete or as continuous. & Nomina, Interval, Ratio or Ordinal: Temperatures in Celsius at different locations in an Italian city.

Quant, Continuous, interval

Classify each of the following as qualitative (categorical) variables or as quantitative variables. For those which are quantitative, further classify as either discrete or continuous Energy usage in a production process

Quant. and Continuous

Qualitative or Quantitative with (discrete / continuous): The number of courses a randomly chosen person registers for in TigerEnroll

Quantative, discrete

Classify each of the following as qualitative (categorical) variables or as quantitative variables. For those which are quantitative, further classify as either discrete or continuous Average test score on a test ranging from 0 to 100

Quantitative, Continuous

In each of the following, classify the resulting data variable as qualitative or as quantitative. If quantitative, label as discrete or as continuous. & Nomina, Interval, Ratio or Ordinal Ex: Birth year of Each of your family

Quantitative, Discrete, Interval

In each of the following, classify the resulting data variable as qualitative or as quantitative. If quantitative, label as discrete or as continuous. The time taken to drink a 12 ounce can of cola

Quantitative, continous

In each of the following, classify the resulting data variable as qualitative or as quantitative. If quantitative, label as discrete or as continuous. Length of a shoelace

Quantitative, continuous

In each of the following, classify the resulting data variable as qualitative or as quantitative. If quantitative, label as discrete or as continuous. The volume of drink in a randomly chosen bottle of water

Quantitative, continuous

In each of the following, classify the resulting data variable as qualitative or as quantitative. If quantitative, label as discrete or as continuous. The weight of a randomly selected high school wrestler

Quantitative, continuous

Classify each of the following as qualitative (categorical) variables or as quantitative variables. For those which are quantitative, further classify as either discrete or continuous Number of boot errors on a computer

Quantitative, discrete

In each of the following, classify the resulting data variable as qualitative or as quantitative. If quantitative, label as discrete or as continuous. The number of M&M's eaten by a randomly selected person over the month of Decmember 2023

Quantitative, discrete ("The number of " = Discrete)

Classify each of the following as to the level of measurement (nominal, ordinal, interval, or ratio). the length of time it takes you to travel to the FHSU campus

Ratio

Identify the data level (nominal, ordinal, interval, or ratio) that best describes each of the following cases: The time it takes for a student to complete a statistics exam.

Ratio level

Seventy-five managers were surveyed for the number of days they spent traveling each year. Extend the frequency table given at the right to include a column for relative frequency. The column should include the values of relative frequency for each given interval of days traveled per year.

Relative freq = Frequency/ TOTAL Frequency

Seventy-five managers were surveyed for the number of days they spent traveling each year. Which of these best describes the shape of the distribution of the data given in the table?

Skewed Right

Which of these best describes the shape of a histogram for the relative frequency column instead of the frequency column?

Skewed right

Calculate the Coefficent Variation:

Standard deviation/ mean

What is a Standard deviation:

Standard deviations is a number to tell how measurments for a group are spread out from the average (mean), or expected value. Specifically, the standard deviation is a type of "average" measure on how all the various data values deviate or differ from the data means. For Instance if the Standard deviation is higher, then that means that there are one or more outliers. vs when its lower.

Number of monthly infections reported at a local hospital averaged 121 with a standard deviation of 6.8. During a recent month, the hospital experienced 139 patients with infections. Assuming the data possesses a bell-shaped distribution, does the 139 patients fall within an interval which contains 95% of the number of patients with infections? Show the sigma rules and explain why or why not?

Step 1: Find SD above mean: 121+(6.8*2) Step 2: Find SD Below Mean: 121- (6.8*2) No 139 does not fall within an interval which contains 95% of the number of patients with infections. 139 is higer than 134.6 showing that its outside of the 95%.

The number of hours worked by 20 FHSU students over the course of one week is given in the table at the right. Create a reasonable frequency table for this data set with exactly 4 classes. Include a relative frequency column in the table. 22 30 29 35 21 26 25 35 20 16 38 31 28 4 27 10 0 36 24 12

Step 1: Calculate the 1: Min --> =min( ) 2: Max --> =max ( ) 3: Class Width --> Max-Min/ 4 <-- this is given to us in the problem. The class width tells us how to make the table, if we split the hours worked into 4 sections. Step 2: Table with Hrs Worked, Frequency, Relative Frequency 2b: Relative frequency = Frequency/ Total Frequency

A doctor is interested in analyzing the increase in systolic blood pressure caused by a certain chemo drug. Would the doctor be more interested in studying the mean, median, or mode of the systolic blood pressures?

The doctor would most likely be more interested in studying the mean and the median, it would be more useful as measures of center for systolic blood pressure.

The motor vehicle manufacturer is trying to decide which colors it should offer for a new sports utility vehicle. In analyzing the preferred colors of other sports utility vehicles, would the manufacturer be more interested in the mean, median, or mode of the colors?

The manufacturer would be more interested in the mode which would help with nominal data.

The marketing director for an advertising agency is trying to target an ad campaign that will be shown in one city only. Would he be more interested in the mean or median family income in the city?

The marketing director will be more interested in the city's median family income because there may be a large gap between salaries and the median is the least affected by outsiders.

A manufacturer makes bags of popcorn and bags of potato chips. The average weight of a bag of popcorn is supposed to be 3.07 ounces with an allowable deviation of 0.02 ounces. The average weight of a bag of potato chips is supposed to be 5.06 ounces with an allowable deviation of 0.04ounces. A factory worker randomly selects a bag of popcorn from the assembly line and it has a weight of 3.04 ounces. Then the worker randomly selects a bag of potato chips from the assembly line and it has a weight of 5.04 ounces. Which description closely matches the findings on the assembly line?

The potato chip baf assembly line is closer to the specifications given because its z score is closer to the standard than the popcorn bag assembly line.

Controlled Experiments:

The purpose of controlled experiments is to reveal the response of one variables (Crop yield, the response variable) to change another (Level of fertilization , the explanatory variable). Researchers attempt to control the environment of the experiment so that the effects of one variable on another can be isolated and measured. There is a control group and an experiment group.

The graph at the right is a bar graph of the distribution of hours spent playing video games over the past week from a collection of randomly selected teenagers in the United States. Answer the following: How many teenagers were part of this study?

There were a total of 1139 teenage males, as shown on right side.

Give an example of a situation where the median is likely a better average to use to describe the center location of quantitative data as compared to the mean.

When a few outliers exist within the data, we might use the median as a best measure of the "center" in the data since the mean is very sensitive to such extreme values. For example we are measuring the communities annual income data and there is a very large gap in the between it. Like most people earn between $20,000-40,000 and there is an one or two outlier that has an annual income of $200,000. A large income gap in income will skew the data greatly even by a small number of wealthy people.

Interpret the meaning of this z-score in the context of the data set. Zscore = -0.14081913

Zscore = -0.14081913 This tells us that the data value of 22 is only 0.14081913 standard deviation below the mean value.

Ratio Data:

are similar to interval data, except that it has a meaningful zero point and the ratio of two data points is meaningful. The operation of addition, subtraction, multiplication and division are reasonable on ratio data. Ex is mone a ratio variable? Say ur friend has 40 bucks and u have 20. 40/20 =2. Your friend has twice as much money. You had to divide to see the ratio. So yes this is a ratio variable.

What is a Variance?

data set contianing the complete set of population data is given.

What is a Population?

is a total set of subjects or things we are interested in studying. Ex: Monkeys in brazil =population Ex: studying Students in a college, pop= students

Identify the data level (nominal, ordinal, interval, or ratio) that best describes each of the following cases: Placement (1st, 2nd, etc.) within a wrestling tournament

ordinal