BA 1 - Describing and summarizing data

What percentile does the median represet?

50% is correct Remember that half of a distribution's data points are less than or equal to the median. Therefore, the median is equal to the 50th percentile, because 50% of the data points are equal to or below this value.

A student finds that there is a positive correlation between the volume of music and the prevalence of acne. The hidden variable is age; teenagers tend to listen to louder music and have more acne.

Example of a hidden variable To determine whether there is a hidden variable, first identify two variables that are not fundamentally related to each other, and then identify a third variable that is correlated with each. In this case, first two variables are acne and music volume. The third variable, age, is related to both. Age is related to acne; with acne decreasing once a person passes adolescence. In addition, age is related to music volume, with younger people tending to listen to louder music. Loud music does not lead to acne or vice-versa.

A researcher finds a positive correlation between the number of traffic lights in a town or city and the number of crimes committed each month in that town. The hidden variable is population. Cities with a greater number of people have more traffic and thus need more traffic lights. These cities also have more people who can commit crimes (and be victims of crimes), and more crimes are committed.

Example of a hidden variable To determine whether there is a hidden variable, first identify two variables that are not fundamentally related to each other, and then identify a third variable that is correlated with each. In this case, the two variables are number of traffic lights and number of crimes. The third variable, population, is related to both. Population is related to traffic lights; higher populations lead to more traffic, which in turn leads to the need for more lights. Population is also related to number of crimes. Even if we hold the crime rate constant, as the population increases, the number of criminals, and thus number of crimes, increase. Traffic lights, however, do not lead to crime or vice-versa.

A hidden variable, such as GDP, may explain variation in oil consumption across various countries, and provide more clarity than looking solely at the number of barrels of oil consumed.

Not an example of a hidden variable

A retail store owner offers a small discount on the same-day delivery service she offers for her store's products. In the week following the discount offer, sales via the delivery service jumped by 50%. The hidden variable is weather; it rained throughout that week and more people opted for delivery rather than going to the store.

Not an example of a hidden variable To determine whether there is a hidden variable, first identify two variables that are not fundamentally related to each other, and then identify a third variable that is correlated with each. Although the weather is probably correlated with the increase in same-day delivery, it is not related to the discount, and so does not function as a hidden variable between weather and the discount.

Market researchers at a corporation assess the sales and revenue for the corporation's hot dog subsidiary, but do not pay attention to the fact that many people in their market are vegetarians. The researchers' lack of understanding about the dietary habits of the market is a hidden variable.

Not an example of a hidden variable To determine whether there is a hidden variable, first identify two variables that are not fundamentally related to each other, and then identify a third variable that is correlated with each. Here there are not two variables that are correlated; there is only one: hot dog sales. Although dietary habits may be hidden from the researchers in a conversational sense, it is not a hidden variable in the statistical meaning of the term.

What can be concluded from the fact that the correlation coefficient between the acceptance rate at the top 100 U.S. MBA programs and the percent of students in those programs who are employed upon graduation is -0.32?

On average, as the acceptance rate decreases, the percent of students employed upon graduation increases. is correct -0.32 is negative which indicates that, on average, as acceptance rate decreases, the percent of students employed upon graduation increases.

A consultant compiled the following data set that shows the number of visits made to the National Museum of American History from 2001 to 2015. The consultant noticed that the number of visits in 2007 and 2008 seemed unusually low compared to the rest of the data set. What should the consultant do about the data points from 2007 and 2008?

Research the data points and then make a decision based on the findings. is correct The consultant should delete or change data points only if careful examination of the data and the data sources indicates that the data points are incorrect or irrelevant to the research at hand. The consultant must use his or her experience and knowledge of the research question to make decisions on a case-by-case basis. Doing business analytics effectively requires judgment. In this case, the National Museum of American History underwent renovations which reduced significantly the number of visits to the museum in 2007 and 2008. The data points for 2007 and 2008 are correct and should not be changed. However, the fact that the museum was closed during most of that two year period should be considered when drawing conclusions from this data set.

Which of the following formulas would calculate the statistic that is MOST APPROPRIATE for comparing the variability of two data sets with different distributions?

Standard Deviation/Mean is correct This is the formula for the coefficient of variation, the best statistic to compute to compare the variability of two data sets with different distributions. Dividing by the mean provides a measure of the distribution's variation relative to the mean.

What percentile does the mean represent?

The answer cannot be determined without further information is correct Remember that the mean's location depends upon the distribution of the data set. Recall how the location of the mean differs for a symmetrical distribution and a skewed distribution. Therefore, there is no way to determine the percentile of the mean without more information about the data set.

What percentile does the mode represent?

The answer cannot be determined without further information is correct Remember that the mode's location depends upon the distribution of the data set. Therefore, there is no way to determine the percentile of the mode without more information about the data set.

An internet marketing firm compiled a data set of the number of seconds website visitors stay on one of its client's homepage before abandoning the site. The firm presented the summary statistics for the data set to the client. The client asked why the mean of the data set is so much larger than the median. Which of the following is most likely true?

The distribution of the data is skewed to the right is correct When the distribution of data is skewed to the right, the mean is most likely greater than the median. The extreme values in the right tail pull the mean towards them.

Which of the following is an example of a hidden variable?

There is a correlation between the number of firefighters who show up at a fire and how much damage the fire causes. The hidden variable is the size of the fire. is correct A hidden variable is one that is correlated with each of two variables that are not fundamentally related to each other. In this case, the size of the fire leads to a call for more firefighters, and the size of the fire also generally leads to more damage. The number of firefighters does not lead to a greater amount of fire damage.