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"Range and Variance" Data Analysis PPT Courseware
Introduce new knowledge
Range: the difference between the largest data and the smallest data in a set of data
Range = maximum value – minimum value.
Function: Range can reflect the range of changes in data.
Range is the simplest quantity that measures changes in data, but it is greatly affected by extreme values.
Tracking exercise one
1. In data statistics, the indicator that can reflect the change range of a set of data is ()
A mean B mode C median D range
2.The range of data 0, -1, 3, 2, 4 is ＿＿＿＿＿.
3. The highest temperature on a certain day is 4 ℃, and the temperature difference is 9 ℃, then the lowest temperature is _____ ℃.
4. The range of the data -1, 3, 0, x is 5, then x =＿＿＿＿＿.
Who has better stability? What data should be used to measure it?
The sum of the deviations between student A’s grades and the average grade:
(85-90)+(90-90)+(90-90)+(90-90)+(95-90)=0
The sum of the deviations between student B’s grades and the average grade:
(95-90)+(85-90)+(95-90)+(85-90)+(90-90)=0
think about it
What else is related to the sum of the squares of the above deviations?
——Related to the number of exams!
Therefore, the average of the squared deviations should be further used to measure the stability of the data.
Assume that in a set of data x1, Use their average, that is, use
S2=1/n[(x1-x)2+ (x2-x)2 +…+ (xn-x)2 ]
Tracking exercise two
1. The function of sample variance is ( )
(A) represents the overall average level
(B) represents the average level of the sample
(C) Accurately represents the overall fluctuation size
(D) represents the fluctuation size of the sample
2. The variance of samples 5, 6, 7, 8, and 9 is _______.
3. The calculation formula of sample variance S2=1/10[(x1-20)²+(x2-20)²+....(xn-20)²]
The number 10 means _______ and the number 20 means _______.
The difference and connection between range and variance:
Connection: Range and variance are both indicators used to measure (or describe) the deviation of a set of data from the mean (i.e., the size of the fluctuation). They are often used to compare the fluctuations of two sets of data.
Difference: Range uses the difference between the maximum value and the minimum value in a set of data to reflect the range of data changes. It mainly reflects the difference between two extreme values in a set of data and is insensitive to fluctuations in other data.
The variance is the result obtained by using the method of "first average, then find the difference, then square, and finally average again". It mainly reflects the fluctuation of the entire set of data. It is an important indicator that reflects the degree of dispersion of a set of data from its average value. Each Changes in the data will affect the variance results.
In actual use, the variance of a set of data is often calculated to measure the fluctuation of a set of data.
Variance can be used for comparison only when the sample sizes of the two sets of data are the same and the means are equal or similar.
The unit of variance is the square of the original data unit.
Do you remember it?
1. The concepts and calculations of range and variance.
2. The variation range of extreme response data,
3. The variance represents the degree of dispersion (fluctuation) of the data. The larger the variance, the more dispersed the data distribution, the larger the fluctuation, and the more unstable it is.
4. Use the sample variance to estimate the population variance
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"Range and Variance" Data Analysis PPT Courseware 2:
"Range and Variance" Data Analysis PPT Courseware 2 Review 1. The variance of data 0, -3, 1, -2, -3, 2, 3 is ( ) A -3 B 3 C -6 D 6 2. Two Basketball players compete in a shooting competition. If the variance of player A's performance is 0.12, the variance of player B's performance is...