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Mathematical problems about mean and median Number: 1 1 2 4 2 3 Annual profit (10000 yuan / person) 2052.52.11.51.51.2 What is the average and median annual profit per person of the company? Quick! Seek the expert solution! Good Bonus!
The average is the sum of all numbers added and divided by the number of numbers, so the average is (20 + 5 + 2.5 * 2 + 2.1 * 4 + 1.5 * 2 + 1.5 * 2 + 1.2 * 3) / (1 + 1 + 2 + 4 + 2 + 2 + 3) = 48 / 15 = 32000, the median is the order of all numbers from small to large, if the number is odd, then the median is the middle number
Median mode mean
concept
The differences between them are mainly shown in the following aspects
1. Different definitions
Average: the quotient obtained by dividing the sum of a group of data by the number of the data is called the average of the data
Median: a group of data in size order, in the middle of a number called the median of this group of data
Mode: the number that appears most frequently in a set of data is called the mode of this set of data
2. Different methods
Average: divide the sum of all data by the number of data, which needs to be calculated
Median: the data are arranged in the order from small to large or from large to small. If the number of data is odd, the number in the middle is the median of this group of data; if the number of data is even, the average of the two data in the middle is the median of this group of data. Its calculation does not need or only needs simple calculation
Mode: the most frequent occurrence number in a set of data, which can be calculated without calculation
3. The number is different
In a group of data, the mean and median are unique, but sometimes the mode is not. In a group of data, there may be more than one mode or no mode
4. Present different
Average: is a "virtual" number, is calculated, it is not the original data in the data
Median: it is an incomplete "virtual" number. When a group of data has an odd number, it is the data in the middle after sorting, which is a real data in the group. However, when the number of data is even, the median is the average of the two data in the middle, which is not necessarily equal to one of the data in the group, The median is a virtual number
Mode: the original data in a set of data, which is real
5. It's different
Average: reflects the average size of a set of data, often used to represent the overall "average level" of data
Median: like a dividing line, the data is divided into the first half and the second half, so it is used to represent the "medium level" of a set of data
Mode: reflects the most frequent occurrence of data, used to represent the "majority level" of a group of data
Although these three statistics reflect different, they can all represent the concentrated trend of data and represent the general level of data
6. Different characteristics
Average: it is related to every data, and the change of any data will cause the change of the average. The main disadvantage is that it is easily affected by extreme value. The extreme value here refers to too large or partial decimal. When there is too large a number, the average will be raised. When there is partial decimal, the average will be reduced
Median: it is related to the arrangement position of data, and the change of some data has no effect on it; it is the representative value in the middle position of a group of data, and is not affected by the extreme value of data
Mode: it is related to the frequency of data occurrence. It focuses on the investigation of the frequency of each data occurrence. Its size is only related to some data in this group of data and is not affected by extreme values. Its disadvantage is that it is not unique. A group of data may have one mode, or multiple or none
7. The function is different
Average: it is the most commonly used representative value of data in statistics. It is more reliable and stable because it is related to each data and reflects the most sufficient information. Average can not only describe the overall average situation of a group of data itself, but also be used as a standard for comparison of different groups of data. Therefore, it is most widely used in life, For example, we often say the average score, average height, average weight and so on
Median: as the representative of a group of data, the reliability is relatively poor, because it only uses part of the data. But when the individual data of a group of data is too large or too small, it is more appropriate to use median to describe the centralized trend of the group of data
Mode: as the representative of a group of data, the reliability is also relatively poor, because it only uses part of the data. In a group of data, if individual data has great changes, and a data appears the most times, it is more appropriate to use the data (i.e. mode) to represent the "centralized trend" of this group of data
The relations and differences among mean, median and mode are as follows
The average is widely used. As the representative of a group of data, it is relatively stable and reliable. But the average is related to all the data in a group of data and is easily affected by extreme data. In short, it represents the average of this group of data. The median is in the middle position in the numerical ranking of a group of data, People can judge and control things by the median. Although it is not affected by extreme data, its reliability is relatively poor. So the median only represents the general situation of this group of data. Mode focuses on the frequency of a group of data. As the representative of a group of data, it is not affected by extreme data, and its size is related to some data in a group of data, In a group of data, if individual data has great changes and a certain data appears more frequently, it is more appropriate to use mode to represent the centralized trend of this group of data, which reflects the centralized situation of the whole data
Average, median and mode have their own advantages and disadvantages
Average: (1) all data of the whole group are needed to calculate;
(2) Vulnerable to extreme values in data
The median: (1) the data can be determined by arranging them in order;
(2) Not susceptible to extreme values in the data
Mode: (1) by counting;
(2) Not susceptible to extreme values in the data
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