MKTG 2340 O'Connor

what formula is used to calculate median of Frequency Distribution?

(N+1)/2

What is the formula needed to calculate the mode of a consecutive series?

(lower value of the modal class)+(Maximum Frequency)-(Frequency preceeded by maximum)/2*(maximum frequency)-(frequency succeeded by maximum)-(Frequency preceeded by maximum)

If the data are qualitative, then the mode is the _____ ______ ________ __ central location

the mode is the only meaningful measure of central location when the data are qualitative

The geometric mean is...

the mulitplicative average of a data set.

What are the 4 steps to find median of Frequency Distribution?

1. Arrange all of the x values in increasing order, write the corresponding f values next to them 2. Find the cumaltive frequency by cumalitively adding all f values 3. Find N by adding all f values together 4. median is the x value corresponding to (N+1)/2 from cumulative frequency column. Whatever cumalitive value is closest to the result of (N+1)/2, find the related x value.

How do you find the mean using the weighted arithmetic method, also known as the Arithmetic Mean Method?

1. Find the median of the elements. If odd select the middle element, if even number of elements, add the two middle elements and divide by two 2. Find the distance from the median element for each element. If elemeents are 1 2 3, the distance would be 1-2=-1, and 3-2 = 1 3. multiply frequency values by the distance from median element. 4. total the values of the frequency and of the (frequency*distance from median element) 5. plug values into the mean formula (median element)+(total of frequency multiplied by median element distance)/(total of frequency)

What values do you need to find from the continuous series of data in order to calculate the mode?

1. Lowest value of the modal class. If modal class is 105-110, lowest value is 105. L=105 2. Maximum fequency. The frequency with the highest value. 3. Frequency preceeded by maximum frequency 4. Frequency succeeded by maximum frequency 5. Width of modal class = largest value - lowest value. 110-105=5

Explain how to calculate the geometric mean

1. list all sample values 2. find the log of each sample value 3. add up all sample value log values, and total 4 divide total log values by number of samples 5. find antilog of the log values/number of samples (10 to the power of (total log values)/(number of samples)

Which of the following characteristics of interest is a variable? 1. The number of degrees in a circle 2. the number of pizzas ordered from Pizza Hut per day 3. The number of months in a year 4. the number of letters in the alphabet

2. the number of pizzas ordered from Pizza Hut per day.

When we calculate the 25th, the 50th, and the 75th percentiles for a data set, we have effectively divided the data into four equal parts, or quarters. Thus, the 25th percentile is also referred to as...

25th percentile = first quartile (Q1) 50th percentile = Second Quartile (Q2) 75th percentile = Third Quartile (Q3)

What is a modal class?

A modal class is x value corresponding to the largest frequency value

A student scores 60 on Exam 1, 70 on Exam 2, and 80 on Exam 3. What is the student's average score for the course if Exams 1, 2, and 3 are worth 25%, 25%, and 50% of the grade, respectively?

A student scores 60 on Exam 1, 70 on Exam 2, and 80 on Exam 3. What is the student's average score for the course if Exams 1, 2, and 3 are worth 25%, 25%, and 50% of the grade, respectively? SOLUTION: We define the weights as w1=0.25, w2=0.25, and w3=0.50. We compute the average score as =0.25(60)+0.25(70)+0.50(80)=72.50. Note that the unweighted mean is only 70 because it does not incorporate the higher weight given to the score on Exam 3.

A __________ is a convenient way to graphically display the five-number summary of a data set.

Boxplot A boxplot is a convenient way to graphically display the five-number summary of a data set.

The covariance and the __________________ ________________ are measures of association that assess the direction and strength of a linear relationhip between two variables

Correlation coefficient

The numerical measure that reveals only the direction of the linear relationship between two variables, but not the strength of the linear relationship, is referred to as the...

Covariance

Cross Sectional data refers to data collected by recording...

Cross Sectional data refers to data collected by recording a characteristic of many subjects at the same point in time, or without regard to differences in time.

We can use the ________ _________ __________ to calculate probabilities for a continuous random variable

Cumulative distribution function

________________ statistics refers to the summary of important aspects of a data set. This includes collecting data, organizing the data, and then presenting the data in the form of _________ and ______

Descriptive statistics, charts and tables

From the scenarios below, indicate the one that best reflects the nominal scale 1. Rank the service at a restaurant on a scale of 1 to 4. 2. Calculate the time it takes a worker to package a product for shipment. 3. Designate males as 0 and females as 1 to compare gender performance on an aptitude test. 4. Note the ages of students in an undergraduate classroom.

Designate males as 0 and females as 1 to compare gender performance on an aptitude test.

Consider the following variable: the number of people in a household. This variable is best categorized as a __________ variable

Discrete varialbe - the number of people can be counted

What is the Cumulative Distribution Function?

For any value of x of the random variable X, f(x), the Cumulative Distribution Function is defined as: F(x)=P(X=<x)

What is a classical probability?

When the chances of an outcome happening or not happening is equal, like in a game of chance, we can reason the probability rather than calculate it. Total number of outcomes of a specific event divided by the total number of outcomes possible.

The ______________ _______________ is a multiplicative average, as opposed to an additive average (the arithmetic mean). It is the relevant measure when evaluating investment returns over several years, as well as when calculating average growth rates.

Geometric Mean The geometric mean is a multiplicative average, as opposed to an additive average (the arithmetic mean). It is the relevant measure when evaluating investment returns over several years, as well as when calculating average growth rates.

The branch of statistics that draws conclusions about a large set of data based on a smaller set of data is often referred to as ______________ statistics.

Inferential

The mean absolute deviation is an average of the absolute differences between the observations and the ___________ of a data set.

Mean

Generally, the ______ is the best measure of central location when outliers are present.

Median

Since the mean can be affected by outliers, we often also calculate the ___________ as a measure of central location.

Median Since the mean can be affected by outliers, we often also calculate the median as a measure of central location.

The ________ of a data set is the value that occurs most frequently

Mode The mode of a data set is the value that occurs most frequently

The ___________ scale represents the least sophisticated level of measurement. If we are presented with this data, all we can do is categorize or group the data. The values in the data set differ merely by name or label

Nominal scale

The mode is the value in the data set that __________ ________ _____ ________ ____________

Occurs with the most frequency

Qualitative data that can be categorized and ranked are measured on the ________ scale

Ordinal scale

The median is the middle value of a data set and is especially useful when _________ ________ _________

Outliers are present

The geometric mean is relevant when summarizing financial returns _____ ______ _____

Over several years

The _______ is the simplest measure of dispersion; it is the difference between the maximum value and the minimum value in a data set

Range The range is the simplest measure of dispersion; it is the difference between the maximum value and the minimum value in a data set

The interval scale is less sophisticated than the ___________ scale.

Ratio

The _________ scale represents the strongest level of measurement. They have a true point zero.

Ratio scale

The notation s^2 represents the...

Sample Variance

The ________ ratio measures the extra reward per unit of risk.

Sharpe Ratio

The standard deviation of a uniform variable function is written as...

SquareRoot(((b-a)^2)/12)

The normal distribution is bell shaped and ____________ around it's mean

Symmetric

The ____________________ is the most widely used measure of central location.

The Mean (Average)

The arithmetic mean is...

The arithmetic mean is the primary measure of central location. Generally, we refer to the arithmetic mean as simply the mean or the average. In order to calculate the mean of a data set, we simply add up the values of all the data points and divide by the number of data points in the population or sample.

The coefficient of variation (CV) for a data set is calculated by...

The coefficient of variation (CV) for a data set is calculated by dividing the standard deviation by the mean

The ______ ___________ _______________ (______) is an average of the absolute differences between the observations and the mean.

The mean absolute deviation (MAD) is an average of the absolute differences between the observations and the mean.

The median is...

The median is the middle value of a data set. It divides the data in half; an equal number of observations lie above and below the median.

the median is calculated as...

The median is the middle value of a data set. The data are arranged in ascending order (smallest to largest) and the median is calculated as The middle value if the number of observations is odd, or The average of the two middle values if the number of observations is even.

A boxplot displays the five-number summary, which are...

The minimum value, first quartile (Q1), Q2, Q3, and the MAX value.

The ________ is the most frequently occurring value in a data set. A data set may have no ______ or more than one _______

The mode is the most frequently occurring value in a data set. A data set may have no mode or more than one mode.

The variance and the _______ _______, are the two most widely used measures of dispersion

The variance and the standard deviation are the two most widely used measures of dispersion.

The ___________ is defined as the average of the squared differences between the observations and the mean.

The variance is defined as the average of the squared differences between the observations and the mean.

A company wants to estimate the mean price of oil over the past 10 years. What type of data does the company need?

Time Series Data

One weakness of the Mean is that it is ___________ ___________ __ ______________

Unduly influenced by outliers

The _________ ________ is relevant when some observations contribute more than others

Weighted Mean The weighted mean is relevant when some observations contribute more than others

continuous uniform distribution

describes a random variable that has an equally likely chance of assuming a value within a specified range

The probability density function for a continuous random variable X has what properties?

f(x)>=0 for all possible values of x of X the area under f(x) over all values x of X equals 1

The geometric mean is the average of a set of products, the calculation of which is commonly used to determine the performance results of an

investment or portfolio.

The geometric mean is _____ sensitive to outliers

less sensitive

Samples are primarily used to...

make inferences about population parameters

When the data is qualitative, and you want to measure the central location, you calculate the _______ of the data.

mode

A ______________ includes all items of interest in a statistical problem.

population

Consider the following variable: the color of a car in a parking lot. This variable is best categorized as a ____________ variable

qualitative - it is described by a color rather than a number

Mean-variance analysis is used to measure the performance of an asset based on its rate of return. Specifically, this means evaluating the rate of return on the basis of...

risk and reward

Sampling, rather than surveying an entire population, can offer the benefit of saving _________ and ________

the benefit of saving money and time

The minimum value (Min), the quartiles (Q1, Q2, and Q3), and the maximum value (Max) are often referred to as...

the five-number summary of a data set.