For each of the hypothetical studies, determine if the data set would be better
ID: 3068567 • Letter: F
Question
For each of the hypothetical studies, determine if the data set would be better summarized by the mean and standard deviation, the median and quartiles, or the mode. At least one summary type will be used more than once. A restaurateur measures the volume of soup served in each cup of soup that is ordered on a specific day. A highway patrol officer records the make of a random subset of 200 cars traveling through a particular stretch of highway to determine the most popular car type A researcher computes the yearly salary of all employees at a large company. The chief officers have much higher salaries than the rest of the employees. An actuary collects data on the reported age at death for residents of her state. A researcher surveys the price of regular gas at all gas stations in his city to determine the most common price Answer Bank mean and standard deviation mode mdian and quartiles
Explanation / Answer
Mean and Standard deviation are the measures of central tendency and spread, that is applied on continuous / numeric variables.Morover, they work best when the data is symmetric.
For eg. for a normally distributed data,by putting one, two, or three standard deviations above and below the mean we can estimate the ranges that would be expected to include about 68%, 95%, and 99.7% of the observations.
Mode is nothing but the most frequent observation in a dataset.It is most appropriate when the variable considered is nominal or categorical.It can also be used for discrete data.
Median and Quartiles are measures of central tendency and spread, similar to mean and standard deviation.However, they are prefered over the latter when the data is non-normal or skewed.Morover median is usually prefered when the variable is ordinal.
1. The variable here is- Volume of soup served per day.(Continuous or numeric type)
The best measure that would summarize the variable is Mean and Standard deviation, as determining the average volume of soup served per day would make more sense.
2.To determine the most popular car type,
Here, the variable (car type) is nominal and one has to find out which is the most popular among them, in other words the most frequent.
Hence the data would be best summarized by Mode.
3.Here, the variable is Salary of the employees, a numeric variable.However, we find that chief officers have much higher salaries than the rest, it provides a hint that the data is skewed.Hence, it would be better, if we prefered Median and Quartiles to Mean and SD.
Hence, the data would be best summarized by Median and Quartiles
4.Here, the variable is Age of death, a numeric variable.Average age of death for residents would be a more useful measure than the rest.
Therefore, the data would be best summarized by Mean and Standard deviation.
5.The variable, here, is price of regular gas at all gas stations.We are asked to determine the most common price, i.e. the most frequently occuring price in the dataset.
Hence the data would be best summarized by Mode.
6.Arranging the histograms in ascending order of the standard deviations:
Standard deviation measures the spread or dispersion of the data points.It is the amount by which the data points differ from their mean value.
Firstly, let us calculate the range of each of the 4 graphs:
Graph Range
1 90-0 = 90
2 90-20 = 70
3 90-10 = 80
4 40-0 = 40
Range gives us a rough idea on the dispersions of datapoints on the graphs.However, this alone would not suffice.We need to take a look at the mean values and how far the extreme values are from their corresponding means.
Let us consider the graph with the smallest range-Graph 4.Here, mean = 18.5.Also, we find that majority of the datapoints (depicted by the tallest bar) lie closer to the mean.
Hence, Graph 4 has the least standard deviation.
Graph with the next smaller range is graph 2.With mean = 62.8, we find that majority of the datapoints lie within the range 50 to 80, near and around 62.8.
Hence, Graph 2 has the next smallest standard deviation.
Now comparing graphs 1 and 3, we know that the standard deviation is usually smaller when the curve is bell shaped.
Hence, graph 1 has smaller standard deviation than graph 3.
Arranging the histograms in ascending order of the standard deviations:
Graph 4 < Graph 2 < Graph1 < Graph 3
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.