Average, first normalize the histogram, that is to say, the sum of the areas of all rectangles is 1, and then the area of each rectangle represents the frequency of the number of midpoints of the abscissa at its bottom, so the area multiplied by the abscissa is equivalent to the frequency multiplied by the abscissa, and of course the average value is obtained.
There is no sample data in the frequency histogram. In a certain group, the sample data distributed in the group cannot be found, and then the distribution is uneven, so the abscissa of the midpoint of the group is used to represent the average value of the sample data of the group.
The area of each small rectangle represents the corresponding frequency (equivalent to the percentage of the corresponding data), so the average value is equal to the sum of the areas of each small rectangle multiplied by the abscissa of the midpoint at the bottom of the corresponding group.
Extended data:
Application of frequency distribution histogram
The histogram of frequency distribution can clearly show the frequency distribution of each group and easily show the frequency difference between each group. It is mainly to express the data we get intuitively and vividly, so that we can better understand the distribution of the data, so the distance between groups and the number of groups play a key role.
If there are too few groups, the data will be very concentrated; If there are too many groups, the data will be scattered, covering up the distribution characteristics. When the data is within 100, it is generally appropriate to divide them into 5~ 12 groups.
Several data can be estimated from the histogram of frequency distribution:
Mode: the abscissa of the midpoint of the bottom of the highest rectangle in the frequency distribution histogram.
Arithmetic average: the median of each group of values in the frequency distribution histogram is multiplied by the frequency and then added.
Weighted average: the weighted average is the sum of all frequencies multiplied by numerical values.
Median: the abscissa of a straight line parallel to the Y axis, which divides the histogram of frequency distribution into two parts with equal area.
References:
Baidu Encyclopedia-Frequency Distribution Histogram