Which of the following measures of central tendency is/are sensitive to extreme values
Please find below some common questions that are asked regarding measures of central tendency, along with their answers. These FAQs are in addition to our article on measures of central tendency found on the previous page. Show
What is the best measure of central tendency?There can often be a "best" measure of central tendency with regards to the data you are analysing, but there is no one "best" measure of central tendency. This is because whether you use the median, mean or mode will depend on the type of data you have (see our Types of Variable guide), such as nominal or continuous data; whether your data has outliers and/or is skewed; and what you are trying to show from your data. Further considerations of when to use each measure of central tendency is found in our guide on the previous page. In a strongly skewed distribution, what is the best indicator of central tendency?It is usually inappropriate to use the mean in such situations where your data is skewed. You would normally choose the median or mode, with the median usually preferred. This is discussed on the previous page under the subtitle, "When not to use the mean". Does all data have a median, mode and mean?Yes and no. All continuous data has a median, mode and mean. However, strictly speaking, ordinal data has a median and mode only, and nominal data has only a mode. However, a consensus has not been reached among statisticians about whether the mean can be used with ordinal data, and you can often see a mean reported for Likert data in research. When is the mean the best measure of central tendency?The mean is usually the best measure of central tendency to use when your data distribution is continuous and symmetrical, such as when your data is normally distributed. However, it all depends on what you are trying to show from your data. When is the mode the best measure of central tendency?The mode is the least used of the measures of central tendency and can only be used when dealing with nominal data. For this reason, the mode will be the best measure of central tendency (as it is the only one appropriate to use) when dealing with nominal data. The mean and/or median are usually preferred when dealing with all other types of data, but this does not mean it is never used with these data types. When is the median the best measure of central tendency?The median is usually preferred to other measures of central tendency when your data set is skewed (i.e., forms a skewed distribution) or you are dealing with ordinal data. However, the mode can also be appropriate in these situations, but is not as commonly used as the median. What is the most appropriate measure of central tendency when the data has outliers?The median is usually preferred in these situations because the value of the mean can be distorted by the outliers. However, it will depend on how influential the outliers are. If they do not significantly distort the mean, using the mean as the measure of central tendency will usually be preferred. In a normally distributed data set, which is greatest: mode, median or mean?If the data set is perfectly normal, the mean, median and mean are equal to each other (i.e., the same value). For any data set, which measures of central tendency have only one value?The median and mean can only have one value for a given data set. The mode can have more than one value (see Mode section on previous page). Chapter 6. Univariate descriptive statistics1. Compute the mode, median, and mean for the following four sets of numbers:
Use this set of numbers for the following questions:
2.Assume the numbers in the data are the answers you get when you ask people "How many magazines do you subscribe to?" What are the proper measures of central tendency and dispersion for this data? Calculate their values.
3. Assume the numbers in the data are the answers you get when you ask people "Name your favorite television program." Then you classify each program according to its thematic content. You use a system that has seven different classes (eg. 1=science fiction, 2=comedy, 3=romance, 4=adventure, 5=news, ....). The numbers in the data indicate which category their favorite programs fall into. What are the proper measures of central tendency and dispersion for this data?
4. Assume the numbers in the data are the answers you get when you ask people "What is your household's annual income? I'm going to read a list of possible ranges, and I want you to stop me when I read the range that describes your household's income." You then read the following list and record their answers:
What are the proper measures of central tendency and dispersion for this data? Calculate their values.
5. Below are the final exam scores in percentages for students in a course on postmodernist approaches to analysis of individual differences in skiing preferences.
a. Which of the measures of central tendency are the most and least appropriate for this data?
b. Which tell you more about the relative performance of males and females on the exam?
c. Discuss the benefits and drawbacks of each measure of central tendency for this data.
d. Compute the range, interquartile range, and standard deviation.
e. Discuss the benefits and drawbacks of each measure of dispersion for this data.
6. Use the table of random numbers (Table 7 in Appendix B) for this question. Use the last two digits of the 5-digit numbers. Starting at the top of the second column, scan down and mark the numbers that are between 10 and 29, including 10 and 29. Do this until you get a total of 15 numbers. Write these 15 two-digit numbers on a piece of
paper. Calculate the median, the mean, and the standard deviation for these numbers. Use the computational equation for standard deviation. 7. Analyze all four sets of numbers in Question 1 in terms of which of the measures of central tendency are the most and least appropriate. For each set of numbers, discuss the benefits and drawbacks of each measure of central tendency. 8. On a mid-term exam, the median score is 73 and the mean is 79. Which student's score is likely to be further away from the median — the one at the top of the class or the one at the bottom? Why?
9. If the standard deviation of a sample is 5.3,
10. Compute the standard deviation, range, and interquartile range for the following data:
11. Multiply each of the nine numbers in Question 11 a by a constant, say 0.4, and calculate the standard deviation. What is the effect on the standard deviation of multiplying the numbers by a constant? Try it with a different constant, say 1.3. What is the effect? What is the general pattern here?
12. Subtract a constant, say 50.0, from each of the nine numbers in Question 11, and calculate the standard deviation. What is the effect on the standard deviation of subtracting a constant? Try it with a different constant, say 63.89. What is the effect? What is the general pattern here?
13. What is the nature of the sample data if s = 0 and n = 75?
Which measure is sensitive to extreme values?The mean is sensitive to all scores in a sample (every number in the data affects the mean), which makes it a more "powerful" measure than the median or mode. The mean's sensitivity to all scores also makes it sensitive to extreme values, which is why the median is used when there are extreme values.
Which of the following measures of central tendency is affected by extreme values?Arithmetic mean takes into account the value of all items (i.e. very large and very small) in a series. Thus, it is only arithmetic mean which is affected by extreme values in the series.
Which of the following measures of central tendency is are sensitive to extreme values quizlet?The measure of central tendency that is more sensitive to outlier is the mean. Mean is directly affected by extreme values because it is the average of all values in a data set.
Which of the following measures of central tendency is most affected by extreme values outliers?Option A is the solution since the mean involves every point in the data set in its calculation, it becomes the measure of central tendency most susceptible to outliers or extreme values.
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