Mode focuses on the frequency of each data, which is the original data in a set of data, and its size is only related to some data in this set of data. When a lot of data in a set of data appear repeatedly, its pattern is often a statistic we care about; Note: Sometimes there is more than one pattern in a set of data. For example, in data 2, 3,-1, 2, l and 3, 2 and 3 all appear twice, and they are all patterns of this set of data.
Median-arrange n data in order of size, and the data in the middle position (or) is called the median of this group of data. The median is only related to the position of data arrangement. When a set of data is arranged from small to large, the middle data is the median (the average of the middle two of even data). Therefore, changes in some data have little effect on the number of digits. When the individual data in a group of data changes greatly, it can be used to describe its concentration trend.
Note: (1) To find the median, a set of data should be sorted by size without calculation. As the name implies, the median is the middle number (or the average of the two middle numbers), which can be sorted from small to large or from large to small.
(2) When the number of data is odd, the median is one of the data in this group; However, when the number of data is even, the number of bits is the average of the middle two data, which is not necessarily equal to one data in the group.
In the same set of data, the mode, median and average also have their own characteristics:
(1) The median and average are unique, but the mode is not unique;
(2) The mode, median and average are generally unequal, and may be equal under special circumstances.
For example, in data 6, 6, 6, 6, 6, the mode, median and average are all 6.
Watch serial number
1
2
three
four
five
six
seven
eight
nine
10
Daily travel time error (seconds)
-2
2
1
-3
- 1
2
four
-3
For example, when inspecting the quality of watches produced by a factory, the inspectors randomly selected 10 watches, and recorded the travel time error of each watch in the table below (a positive number means faster than the standard time, and a negative number means slower than the standard time). Do you think it is appropriate to use the average error of this 10 table to measure the accuracy of this 10 table?
Solution: [(-2)+0+1+(-3)+(-1)+0+2+4+(-3)+2] ÷10 = 0 ÷/kloc-0.
Judging from this average value, it seems that all the watches of 10 are accurate and have no errors, but in fact, there are 8 watches with errors. The fact that individual watches have errors is covered by the average value, so the median value can better reflect the problem.
For another example, in order to prepare for the fraternity in the class, the monitor made a public opinion survey about what kind of fruit the class likes to eat and what fruit to buy at last. Please think about it. Should this question be decided by the average, median or mode in the survey data? It is undoubtedly determined by the mode, because the median or average number of people who like all kinds of fruits is meaningless.