From the number set 1, 2, 3, 4, I can tell that the range is 3, The mean is 2.5, the median is 2.5, yet there is absolutely no mode.
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The statistical mode of a set of numbers is the number(s) that occur the most times. There is no mode for a single number. If the set of numbers was 3, 4, 1, 3, 5, 2, for example, the mode is 3, since it occurs twice.
Mode: "most"- The number that occurs the most. There isn't always a mode. Example: 1, 2, 2, 6,2,5,6, 7,6,4,9,5,8,2 The number 2 is the mode because it occurs most frequently. The mode need not be a number, you can have a mode with qualitative data. RED RED BLUE GREEN. The mode is RED. Mean: This is the arithmetic average. If there are n numbers, you add them up and divide by n, this is the mean. For example if n=3, there are 3 numbers. Let's say they are 1, 2, and 3. Add them up and you have 6, divide by 3 and the mean is 2. Median: If the numbers are placed in ascending order, this is the number in the middle if you have an odd number of numbers (entries). If you have an even number of numbers, the median is the mean of the two middle numbers. For example, 1 2, 3, the median is 2. Now look at 1, 2, 3, 4. The median is the average of 2 and 3 which is 2.5 even though this is not one of the numbers in the set. There is some controversy over this and some people do it differently, but this method is most commonly used. It is also the one used by the TI 83 calculator.
mean= 2, mode= 1 and 3, median= 3, and range= 2
I am guessing you are asking for an example of a set of numbers with these properties. Let's start with 5 numbers, so the median will be the middle number; say 1, 2, 3, 4, 5. The median is 3, but so is the mean. Now let's replace the 5 with 10. The median is still 3, but the mean is 4. To make the mode less than 3, let us change the 2 into a 1. Now the median is still 3, the mode is 1, and the mean is 3.8. So 1, 1, 3, 4, 10 will work.
The range is the spread of data - the largest number minus the smallest. The mean, mode and median are types of average. The mean is the sum of the numbers divided by the number of numbers (e.g. the mean of 1, 1, 3, 5 and 8) is 3.6). The mode is the number that appears most often (1 for the previous example). The median is the 'middle number'. To work it out, place the numbers in order from lowest to highest. If the number of numbers is odd, the median is the number in the middle (3 for the given example). If the number of numbers is even, the median is the mean of the two middle numbers (e.g. for 1, 1, 3 and 5, the middle numbers are 1 and 3 so the median is 2). The mean and median often are similar but the mode is often greatly different to the two other averages.