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"The Dispersion Degree of Data" PPT courseware
Review the past and learn the new
1. Average
x=1/n(x1+x2+x3+····+xn)
2. Mode
In a set of data, the data that appears most often is called the mode of the set of data.
3. Median
Arrange a set of data from small to large, and the middle number (or the average of the two middle numbers) is called the median of the set of data.
The results of the two athletes A and B of the Times Middle School track and field team in 8 100-meter run training are as shown in the table above.
(1) In these 8 training sessions, what are the average, mode, and median of the 100-meter running results of athletes A and B?
The average time of athletes A and B in the 100-meter run is both 12.5 seconds, the median time is 12.45 seconds, and the mode mode is 12.2 seconds.
(2) Xiao Liang said: "The average and mode median of the 100-meter running results of two athletes A and B are the same, so their results are the same." Do you think this statement is appropriate?
Not suitable.
(3) Which athlete's performance do you find has greater fluctuations? Whose results are more stable? From this, do you think that by analyzing a set of data and only caring about the mean, mode, and median of this set of data, you can get the previous conclusion?
Athlete A's training performance has more data that deviates from the average performance, and the fluctuation range is relatively large, while athlete B's performance is relatively stable. For a set of data, it is not enough to just understand the central tendency of the data. You also need to understand the fluctuation range of these data and the degree of deviation from the average.
The difference between the maximum data and the minimum data in a set of data is called the range, that is,
Range = maximum data - minimum data.
The range of athlete A’s 100-meter run is: 13.1-12.0 = 1.l (second);
The range of athlete B's 100-meter run is: 12.9-12.2 = 0.7 (seconds),
Therefore, athlete B's performance is relatively stable.
We usually use the degree of data dispersion to describe the fluctuation range of a set of data and the degree of difference from the average.
The greater the degree of dispersion of the data, the wider the range of the data distribution, the more unstable it is, and the less representative the average is;
The smaller the degree of discreteness of the data, the more concentrated the distribution of the data, the smaller the range of variation, and the greater the representativeness of the average.
In actual life and production, in addition to caring about the central tendency of the data (mean, median, mode), we also pay attention to the degree of dispersion of the data, that is, the degree to which a set of data deviates from the mean.
Class summary
1. For a set of data, it is not enough to only understand the central tendency of the data. You also need to understand the fluctuation range of these data and the degree of deviation from the average.
2. We usually use the degree of data dispersion to describe the fluctuation range of a set of data and the degree of difference from the average.
The greater the degree of dispersion of the data, the wider the range of the data distribution, the more unstable it is, and the less representative the average is;
The smaller the degree of discreteness of the data, the more concentrated the distribution of the data, the smaller the range of variation, and the greater the representativeness of the average.
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