Mean, Median, Mode, and Range
The range of a list a numbers is just the difference between the largest and smallest values. Find the mean, median, mode, and range for the following list of values: 13, 18, 13, 14, 13, 16, 14, 21, 13, but you don\’t have to use this formula. You can just count in from both ends of the list until you meet in the middle, if you prefer, especially if your list is short. Either way will work. Find the mean, median, mode, and range for the following list of values: 1, 2, 4, 7 The values in the list above were all whole numbers, but the mean of the list was a decimal value. Getting a decimal value for the mean (or for the median, if you have an even number of data points) is perfectly okay; don\’t round your answers to try to match the format of the other numbers. Find the mean, median, mode, and range for the following list of values: 8, 9, 10, 10, 10, 11, 11, 11, 12, 13 As you can see, it is possible for two of the averages (the mean and the median, in this case) to have the same value. But this is not usual, and you should not expect it. Note: Depending on your text or your instructor, the above data set may be viewed as having no mode rather than having two modes, because no single solitary number was repeated more often than any other. I\’ve seen books that go either way on this; there doesn\’t seem to be a consensus on the right definition of mode in the above case.
So if you\’re not certain how you should answer the mode part of the above example, ask your instructor before the next test. About the only hard part of finding the mean, median, and mode is keeping straight which average is which. Just remember the following: (In the above, I\’ve used the term average rather casually. The technical definition of what we commonly refer to as the average is technically called the arithmetic mean : adding up the values and then dividing by the number of values. Since you\’re probably more familiar with the concept of average than with measure of central tendency, I used the more comfortable term. ) 87, 95, 76,. He wants an or better overall. What is the minimum grade he must get on the last test in order to achieve that average? We use statistics such as the, and to obtain information about a from our set of observed values. The mean (or average) of a set of data values is the of all of the data values divided by the number of data values. That is: Find the mean of this set of data values. So, the mean mark is 15. Symbolically, we can set out the solution as follows: So, the mean mark is 15. The median of a set of data values is the middle value of the data set when it has been arranged in ascending order.
That is, from the smallest value to the highest value. Find the median of this set of data values. The fifth data value, 36, is the middle value in this arrangement. If the number of values in the data set is even, then the median is the average of the two middle values. The number of values in the data set is 8, which is even. So, the median is the average of the two middle values. There are 8 values in the data set. The fourth and fifth scores, 16 and 17, are in the middle. That is, there is no one middle value. Half of the values in the data set lie below the median and half lie above the median. The median is the most commonly quoted figure used to measure property prices. The use of the median avoids the problem of the mean property price which is affected by a few expensive properties that are not representative of the general property market. The mode of a set of data values is the value(s) that occurs most often. The mode has applications in printing. For example, it is important to print more of the most popular books; because printing different books in equal numbers would cause a shortage of some books and an oversupply of others. Likewise, the mode has applications in manufacturing. For example, it is important to manufacture more of the most popular shoes; because manufacturing different shoes in equal numbers would cause a shortage of some shoes and an oversupply of others.
The mode is 48 since it occurs most often. It is possible for a set of data values to have more than one mode. If there are two data values that occur most frequently, we say that the set of data values is bimodal. If there is no data value or data values that occur most frequently, we say that the set of data values has no mode. The, and of a data set are collectively known as measures of central tendency as these three measures focus on where the data is centred or clustered. To analyse data using the mean, median and mode, we need to use the most appropriate measure of central tendency. The following points should be remembered: The mean is useful for predicting future results when there are no extreme values in the data set. However, the impact of extreme values on the mean may be important and should be considered. E. g. The impact of a stock market crash on average investment returns. The median may be more useful than the mean when there are extreme values in the data set as it is not affected by the extreme values. The mode is useful when the most common item, characteristic or value of a data set is required. ,