8类RD Sharma解决方案–第24章数据处理II(数据以直方图的图形表示)–练习24.1 |套装2

第24章数据处理II(数据以直方图的图形表示形式)–练习24.1 |套装1

问题7.绘制一个直方图来表示以下数据：

Monthly Salary (in Rs)	No. of Teachers
5600 – 5700	8
5700 – 5800	4
5800 – 5900	3
5900 – 6000	5
6000 – 6100	2
6100 – 6200	3
6200 – 6300	1
6300 – 6400	2

解决方案：

To draw a histogram first construct x-axis and y-axis, where the x-axis represents monthly salary (in Rs) and y-axis represents the no. of teachers. Now, by taking suitable intervals from the given frequency table, we construct the rectangles as shown in the below figure. 

问题8.以下直方图显示了城镇中10至40岁年龄段的识字女性人数：

(i)写出识字的女性人数最高的年龄组。

(ii)班级宽度是多少?

(iii)最低频率是多少?

(iv)班级的等级标志是什么?

(v)在哪个年龄段识字的女性最少?

解决方案：

(i) The highest rectangle corresponds to the highest number of literate females, which lies in the interval corresponding to 15−20 years.

(ii) According to the histogram the class intervals are 10−15, 15−20, 20−25, 30−35, 35−40. Therefore, the class width is 5.

(iii) The lowest frequency 320.

(iv) The class mark of the classes is the mid-point of the class interval.

i.e., Class mark = (upper limit + lower limit) / 2

Therefore, the class mark of each class is as given in the table:

Class Interval	Class Marks
10 – 15	12.5
15 – 20	17.5
20 – 25	22.5
25 – 30	27.5
30 – 35	32.5
35 – 40	37.5

(v) The lowest rectangle corresponds to the least number of literate females, which lies in the interval 10−15 years.

问题9.以下直方图显示了工厂工人的月工资(以卢比为单位)：

(i)在哪个工资组中保留最多的工人?他们的电话号码是多少?

(ii)最少的工人工资是多少?这些工人有多少?

(iii)工人总数是多少?

(iv)工厂规模是多少?

解决方案：

(i) From the given figure, the highest rectangle corresponds to the largest number of workers. The required interval is, therefore, Rs 950−1000. There are 8 workers in this interval.

(ii) In the histogram the lowest rectangle corresponds to the least number of workers, so the required interval is Rs 900−950 and there are 2 workers in this interval.

(iii) The total number of workers is the sum of workers in all the intervals, which is:

Total workers = 3 + 7 + 5 + 4 + 2 + 8 + 6 + 5 = 40 workers

(iv) According to the histogram the factory intervals are 750−800, 800−850, …, 1050−100. Hence, the required factory size is 50.

问题10：以下是描述一班43名学生获得的成绩的直方图：

(i)写出获得最高分的学生人数。

(ii)班级人数是多少?

解决方案：

(i) In the given histogram, 

The interval with the highest marks is 90−100.

Three students are there in this interval because the height of the rectangle (90−100) is 3 units.

(ii) According to the histogram the class intervals are 10−20, 20−30, …, 90−100. Therefore, the class size is 10.

问题11.以下直方图显示了学校中22位教师的年龄频率分布：

(i)学校中最大和最年轻的老师人数是多少?

(ii)哪个年龄段的老师在学校里较多，哪个最少?

(iii)每班人数多少?

(iv)班级的等级标志是什么?

解决方案：

(i) The number of the eldest teacher = 1 and the number of the youngest teacher = 2.

(ii) The teachers in age group 35-40 is most and the teachers in age group 50-55 is least.

(iii) Size of classes = 5.

(iv) The class marks of class 20-25 = $\frac{20+25}{2}$ = 45/2 = 22.5. 

The class marks of class 25-30 = 27.5

The class marks of class 30-35 = 32.5

The class marks of class 35-40 = 37.5

The class marks of class 40-45 = 42.5

The class marks of class 45-50 = 47.5

The class marks of class 50-55 = 52.5

问题12：给出了工厂中30名工人的每周工资：

830、835、890、810、835、836、869、845、898、890、820、860、832、833、855、845、804、808、812、840、885、835、835、836、878， 840、868、890、806、840

使用提示标记将频率表的间隔标记为800-810、810-820，依此类推。另外，绘制直方图并回答以下问题：

(i)哪一组工人人数最多?

(ii)多少工人的收入为850卢比以上?

(iii)有多少工人的收入低于850卢比?

解决方案：

The frequency table will be as given below:

Wages (in Rs)	No. of workers
800-810	3
810-820	2
820-830	1
830-840	9
840-850	5
850-860	1
860-870	3
870-880	1
880-890	1
890-900	4
Total	30

Now we draw a histogram, in which x-axis represent wages (in Rs) and y-axis represents the number of workers. Now, by taking suitable intervals from the given frequency table, we construct the rectangles as shown in the below figure. 

(i) Maximum number of workers are present in 830-840 wage group

(ii) Number of workers earn Rs 850 and more = 1 + 3 + 1 + 1 + 4 = 10

(iii) Number of workers earn less than Rs 850 = 3 + 2 + 1 + 9 + 5 = 20