A statistical question about mean and standard deviation

1.This problem is equivalent to finding the 92% quantile of the normal distribution (72, and the score above the 92% quantile gives a, and let the 92% quantile of the normal distribution be x

x-72), where is the standard 92% quantile of the positive ether, which can be obtained by looking up the table or calculator, calculated as x=

2.In the same way, this is equivalent to finding 1-(8%+20%+42%)=30% quantile, and the same method is calculated:

x-72)/

where is the standard positive 30% percentile, calculated as x=

3.In the same way, find the quantile of 1-(8%+20%+42%+18%)=12%.

x-72), where is the standard Zhengtai 12% quantile, calculated x=good luck!

The first sentence of the original question is crucial, "The average grade approximates a normal distribution with a mean of 72 and a standard deviation".

Let f(x) be a distribution function of a standard normal distribution.

x is the grade point average.

then p = f(x)

x(a)=f^(-1)(

x(a)-72<, x(a)=72+

Later, the top 8% is A, the next 20% is B, the next 42% is C, the next 18% is D, and the last 12% is F.

x(c)=f^(-1)(,x(c)-72<, x(c)=72+

x(d)=f^(-1)(,x(d)-72<,x(d)=72+

Note: f(-1)(,f(-1)(,f(-1)(,f(-1) (can be found in the table of standard normal distribution functions.)

The standard deviation of the mean is a measure of the degree to which the distribution of data is dispersed, and is used to measure the degree to which the data values deviate from the arithmetic mean. The smaller the standard deviation, the less these values deviate from the mean and vice versa. The magnitude of the standard deviation can be measured by the magnification of the standard deviation versus the mean value.

The standard deviation is the square root of the arithmetic mean of the square of the deviation of the standard value of each unit of the population from its mean, and is denoted by , and the standard deviation is the arithmetic square root of the variance.

Standard deviation measurement method

Standard deviation, also known as standard deviation or root mean square deviation, is a statistical indicator that reflects the degree of dispersion of a set of measured data. It refers to the magnitude of the fluctuation of the error of the statistical result in a certain period of time. It is one of the important parameters of normal distribution.

It is a statistical measurement method for measuring changes. It is usually not used as a stand-alone indicator but in conjunction with other indicators.

Standard deviation has been widely used in error theory, quality management, metrology, sampling inspection and other fields. Therefore, the calculation of the standard deviation is very important, and its accuracy has a significant impact on the uncertainty of the instrument, the uncertainty of the measurement, and the quality of the product received. However, in the calculation of standard deviation, many people use the Bessel formula regardless of the number of measurements.

Standard deviation is most commonly used in probability statistics as the degree of statistical distribution, and can also reflect the degree of dispersion of a data set. The standard deviation of two sets of data with the same mean may not be the same.

a Standard.

The greater the difference, the better the representation of the average.

b The smaller the standard deviation, the better representative the mean.

c The mean is large and the standard deviation is also large.

d The mean is small and the standard deviation is small.

Correct answer B analysis.

Analysis] Mean and standard deviation are a pair of interrelated statistical indicators used to describe the overall characteristics of data. The mean reflects the trend in the data set, and the standard deviation reflects the trend in the middle of the data. The combination of the two can comprehensively and accurately reflect the overall characteristics of the data.

The greater the standard deviation, the less representative the mean is; Conversely, the average is more representative.

Summary. The hypothesis test of the difference between the sample mean and the population mean is also called the significance test of the population mean. If the difference between the mean of a sample and the mean of the population reaches a significant level, the null hypothesis can be overturned and the sample is not from that population, but from other populations; If the difference between the sample mean and the population mean does not reach a significant level, the null hypothesis is accepted, at which point the sample must be admitted to be from the population.

Mean Standard Deviation (MEAN SD), how to judge significance.

The hypothesis test of the difference between the sample mean and the population mean is also called the significance test of the population mean. If the difference between the mean of a sample and the mean of the population reaches a significant level, the null hypothesis can be overturned, believing that the sample is not from this population, but from other populations. If the difference between the sample mean and the population mean does not reach a significant level, the null hypothesis is accepted, at which point the sample must be admitted to be from the population.

Steps: Hypothesis testing generally begins with the formulation of a null hypothesis and an alternative hypothesis.

Then, the morphology of the probability distribution of a statistic is analyzed if the null hypothesis is true.

The standard deviation of the mean is relative to the standard deviation of a single measurement, and is used as a criterion in the normal distribution curve of random error to describe the degree of dispersion

Under certain measurement conditions (the true value is unknown), multiple groups of measurements (each group is measured n times) of the same measured geometric quantity, then there is an arithmetic mean for each group of n measurements, and the arithmetic mean of each group is different. However, they are much less dispersed than a single measurement. The standard deviation can also be used to describe their degree of dispersion.

According to the error theory, there is a relationship between the standard deviation of the arithmetic mean of the measurement column and the standard deviation of the single measurement of the measurement column. σχ=n

The residual error i is the difference between the measured value and the arithmetic mean.

n: the number of measurements.