Mean, Median, and Mode Practice Problems. Once you complete the practice activity, check to see how well you did by selecting the following link:. Solutions: Mean, Median, and Mode. In this lesson, you have learned how to calculate the mean, median, and mode of a set of data values. In addition, you have been introduced to other key terms such as measures of central tendency, unimodal, bimodal, and outliers. You also learned that the mode is the only measure of central tendency used in both quantitative and qualitative data.
As with every lesson and module, you are encouraged to research how these topics pertain to your particular area of study within the world of information technology. By now you are very aware that not every topic in mathematics will be directly implemented in your future career field. However, do not rule out the possibility that this topic might be an integral part of your future until you do some research. Additional Attributions. Course Home Lessons. Introduction: Connecting Your Learning In real-world applications, you can use tables and graphs of various kinds to show information and to extract information from data that can lead to analyses and predictions.
Focusing Your Learning Lesson Objectives By the end of this lesson, you should be able to: Compute the mean, median, and mode of a given set of data.
Identify an outlier given a set of data. Identify the mode or modes of a data set for both quantitative and qualitative data.
Move Close Print. The mean age of all 8 employees is Use the ages 55, 29, and 46 for one sample of 3, and the ages 34, 41, and 59 for another sample of 3: The mean age of the first group of 3 employees is The mean age of the second group of 3 employees is The average number of hits Mark's Web site has received per day since it was launched is The following numbers represent the number of hours Stephen has worked on this Web site for each of the past 7 months: 24, 25, 31, 50, 53, 66, 78 What is the mean average number of hours that Stephen worked on this Web site each month?
Step 1: Add the numbers to determine the total number of hours he worked. Step 2: Divide the total by the number of months. Find the mean age of his workers if the ages of the employees are as follows: 55, 63, 34, 59, 29, 46, 51, Step 1: Add the numbers to determine the total age of the workers. Answer Move Close Print The mean age of all 8 employees is Driving Times minutes 0 to less than 10 10 to less than 20 20 to less than 30 30 to less than 40 40 to less than Number of Employees 3 10 6 4 2.
Step 1: Determine the midpoint for each interval. For 0 to less than 10, the midpoint is 5. For 10 to less than 20, the midpoint is For 20 to less than 30, the midpoint is For 30 to less than 40, the midpoint is For 40 to less than 50, the midpoint is Step 2: Multiply each midpoint by the frequency for the class.
Answer Move Close Print Each employee spends an average mean time of Find the median of the following data: 12, 2, 16, 8, 14, 10, 6. Answer Move Close Print The median is Find the median of the following data: 7, 9, 3, 4, 11, 1, 8, 6, 1, 4. Answer Move Close Print The median is 5.
Find the mode of the following data: 76, 81, 79, 80, 78, 83, 77, 79, 82, Answer Move Close Print The mode is The ages of 12 randomly selected customers at a local Best Buy are listed below: 23, 21, 29, 24, 31, 21, 27, 23, 24, 32, 33, 19 What is the mode of the above ages? Answer Move Close Print The modes are 21, 23, and The mean, median and mode are all equal; the central tendency of this data set is 8.
Skewed distributions In skewed distributions, more values fall on one side of the center than the other, and the mean, median and mode all differ from each other. One side has a more spread out and longer tail with fewer scores at one end than the other. The direction of this tail tells you the side of the skew. In this histogram, your distribution is skewed to the right, and the central tendency of your data set is on the lower end of possible scores.
In this histogram, your distribution is skewed to the left, and the central tendency of your data set is towards the higher end of possible scores. Mode The mode is the most frequently occurring value in the data set. To find the mode, sort your data set numerically or categorically and select the response that occurs most frequently.
The mode is most applicable to data from a nominal level of measurement. Nominal data is classified into mutually exclusive categories, so the mode tells you the most popular category. For continuous variables or ratio levels of measurement, the mode may not be a helpful measure of central tendency. In this data set, there is no mode, because each value occurs only once.
What is your plagiarism score? Compare your paper with over 60 billion web pages and 30 million publications. Scribbr Plagiarism Checker. To find the median, you first order all values from low to high. Then, you find the value in the middle of the ordered data set — in this case, the value in the 4th position.
You use different methods to find the median of a data set depending on whether the total number of values is even or odd. Median: milliseconds.
Then, find their mean. That means the middle values are the 3rd value, which is , and the 4th value, which is To get the median, take the mean of the 2 middle values by adding them together and dividing by two. The arithmetic mean of a data set is the sum of all values divided by the total number of values. Mean: milliseconds. Outliers can significantly increase or decrease the mean when they are included in the calculation.
Since all values are used to calculate the mean, it can be affected by extreme outliers. An outlier is a value that differs significantly from the others in a data set. For example, consider measuring 30 peoples' weight to the nearest 0. How likely is it that we will find two or more people with exactly the same weight e. The answer, is probably very unlikely - many people might be close, but with such a small sample 30 people and a large range of possible weights, you are unlikely to find two people with exactly the same weight; that is, to the nearest 0.
This is why the mode is very rarely used with continuous data. Another problem with the mode is that it will not provide us with a very good measure of central tendency when the most common mark is far away from the rest of the data in the data set, as depicted in the diagram below:. In the above diagram the mode has a value of 2. We can clearly see, however, that the mode is not representative of the data, which is mostly concentrated around the 20 to 30 value range.
To use the mode to describe the central tendency of this data set would be misleading. We often test whether our data is normally distributed because this is a common assumption underlying many statistical tests. An example of a normally distributed set of data is presented below:. When you have a normally distributed sample you can legitimately use both the mean or the median as your measure of central tendency.
In fact, in any symmetrical distribution the mean, median and mode are equal. However, in this situation, the mean is widely preferred as the best measure of central tendency because it is the measure that includes all the values in the data set for its calculation, and any change in any of the scores will affect the value of the mean.
This is not the case with the median or mode. We find that the mean is being dragged in the direct of the skew. In these situations, the median is generally considered to be the best representative of the central location of the data. The more skewed the distribution, the greater the difference between the median and mean, and the greater emphasis should be placed on using the median as opposed to the mean. A classic example of the above right-skewed distribution is income salary , where higher-earners provide a false representation of the typical income if expressed as a mean and not a median.
If dealing with a normal distribution, and tests of normality show that the data is non-normal, it is customary to use the median instead of the mean. However, this is more a rule of thumb than a strict guideline. Sometimes, researchers wish to report the mean of a skewed distribution if the median and mean are not appreciably different a subjective assessment , and if it allows easier comparisons to previous research to be made.
Please use the following summary table to know what the best measure of central tendency is with respect to the different types of variable. For answers to frequently asked questions about measures of central tendency, please go the next page.
Measures of Central Tendency Introduction A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data. Mean Arithmetic The mean or average is the most popular and well known measure of central tendency. When not to use the mean The mean has one main disadvantage: it is particularly susceptible to the influence of outliers.
Median The median is the middle score for a set of data that has been arranged in order of magnitude. In order to calculate the median, suppose we have the data below: 65 55 89 56 35 14 56 55 87 45 92 We first need to rearrange that data into order of magnitude smallest first : 14 35 45 55 55 56 56 65 87 89 92 Our median mark is the middle mark - in this case, 56 highlighted in bold. So, if we look at the example below: 65 55 89 56 35 14 56 55 87 45 We again rearrange that data into order of magnitude smallest first : 14 35 45 55 55 56 56 65 87 89 Only now we have to take the 5th and 6th score in our data set and average them to get a median of
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