What Is a Cumulative Frequency Histogram?

Frequency histogram is also called frequency distribution histogram . A graph representing the frequency distribution in statistics. In the rectangular coordinate system, the value of the random variable is represented by the horizontal axis. Each cell on the horizontal axis corresponds to the group distance of a group as the bottom edge of the small rectangle. The vertical axis represents the ratio of the frequency to the group distance and uses it As the height of a small rectangle, a set of diagrams composed of such small rectangles is called a frequency histogram .

Assume

Is overall

A sample of

, The maximum value is denoted as b, and

Is less than

The largest integer

Is the smallest integer greater than b, the interval

Divided into m cells

Obviously, the length of each cell is

, And then count the sample observations that fall within each cell.

[Example 1] The average temperature data of April and April in a certain area for 50 consecutive years is as follows (unit: ):

6.9 4.1 6.6 5.2 6.4 7.9 8.6 3.0 4.4 6.7

7.1 4.7 9.1 6.8 8.6 5.2 5.8 7.9 5.6 8.8

8.1 5.7 8.4 4.1 6.4 6.2 5.2 6.8 5.6 5.6

6.8 8.2 6.4 4.8 6.9 7.1 9.7 6.4 7.3 6.8

7.1 4.8 5.8 6.5 5.9 7.3 5.5 7.4 6.2 7.7

Based on the above data, the distribution type of the average temperature in April in this area was inferred.

Solution: minimum value in sample observations

, Maximum

,take

. Interval

It is equally divided into 7 small cells with a length of 1. The frequency and frequency of the sample observations falling into each small cell are calculated, as shown in Table 1.

Table 1

Interval	Frequency	frequency
[3,4]	1	1/50
(4,5)	6	6/50
(5,6)	11	11/50
(6,7)	15	15/50
(7,8)	9	9/50
(8,9)	6	6/50
(9,10)	2	2/50

Make a frequency histogram according to Table 1, as shown in Figure 1. As can be seen from the histogram, the average temperature in April in this area is approximately normal.

figure 1

This conclusion is only a statistical analysis of the sample data, and a hypothesis is proposed for the overall distribution form. Whether it is in line with reality or not needs to be tested.

Note : You can distinguish between frequency histogram and frequency histogram according to the vertical axis.

Difficult point : get the digital characteristics (mean, median, mode, etc.) from the frequency histogram.

[Example 2] Divide the data in a sample of capacity n into 6 groups and draw a frequency distribution histogram. If the frequency ratio of the first group to the sixth group of data is 2: 3: 4: 6: 4: 1, and The sum of the frequencies of the first three sets of data is equal to 27, then n is equal to ().

(A) 80 (B) 75 (C) 70 (D) 65 (E) 60

Solution : frequency = frequency / total, so frequency ratio = frequency ratio, so capacity

Select (E) ^[2] .

[Example 3] In order to understand the quality of a batch of cotton, a cotton spinning mill randomly selected the length of 100 cotton fibers (the length of cotton fibers is an important indicator of cotton quality), and the obtained data are in the interval

The frequency distribution histogram is shown in Fig. 2. Among the 100 samples sampled, the cotton fiber has a length of less than 20 mm ().

(A) 18 (B) 20 (C) 22 (D) 25 (E) 30

Solution : The sum of frequencies less than 20 mm is (0.01 + 0.01 + 0.04) × 5 = 0.3, so there are 30 out of 100, choose E ^[2] .