问题1.一组球队在10场比赛中打进以下进球数：
2，3，4，5，0，1，3，3，4，3
查找这些分数的平均值，中位数和众数
解决方案：
Mean = Sum of all the elements/total number of elements
Mean = (2 + 3 + 4 + 5 + 0 + 1 + 3 + 3 + 4 + 3) / 10
Mean = 2.8
Now calculating Median:
Arranging the given data in ascending order, we get,
0, 1, 2, 3, 3, 3, 3 4, 4, 5
Median = (3 + 3) / 2 = 3
For mode, we will count the element occurring the maximum number of times.
Hence, the mode is 3.
问题2.在对15名学生进行的数学测试中，记录了以下分数(满分100分)：
41、39、48、52、46、62、54、40、96、52、98、40、42、52、60
查找此数据的均值，中位数和众数。
解决方案：
Mean = Sum of all the elements/total number of elements.
Mean = (41 + 39 + 48 + 52 + 46 + 62 + 54 + 40 + 96 + 52 + 98 + 40 + 42 + 50 + 60) / 15
Mean = 54.8
Now we have to find the median:
Arranging the given data in ascending order, we get,
39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98
Here the number of elements is n = 15
Thus, the middle element is the median = 52
Mode = Element 52 occurs 3 times, which is the maximum number of times.
Hence, Mode = 52
问题3.以下意见是按升序排列的。如果数据的中位数为63，则找到x的值。
29、32、48、50，x，x + 2、72、78、84、95
解决方案：
Here, the data is already in ascending order.
Since n = 10 (an even number)
∴ Median is the average of the middlemost two elements.
Since median = 63 as given in the question
∴ (x + x + 2) / 2 = 63
∴ x = 63 – 1 = 62
Hence, the value x is 62.
问题4.找到14、25、14、28、18、17、18、14、23、22、14、18的模式。
解决方案：
When we arrange the data in ascending order, we get,
14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28.
Since data 14 is occurring the maximum number of times.
Hence, the required mode of the given data = 14
问题5.从下表中找到工厂的60名工人的平均工资：
| Salary (in ₹) | Number of workers |
|---|---|
| 3000 | 16 |
| 4000 | 12 |
| 5000 | 10 |
| 6000 | 8 |
| 7000 | 6 |
| 8000 | 4 |
| 9000 | 3 |
| 10000 | 1 |
| Total | 60 |
解决方案：
Calculation table based on the given data:
|
Salary (in Rs.)(xi) |
No. of workers(fi) |
fixi |
|---|---|---|
|
3000 |
16 |
3000 * 16 = 480000 |
|
4000 |
12 |
4000 * 12 = 48000 |
|
5000 |
10 |
5000 * 10 = 50000 |
|
6000 |
8 |
6000 * 8 = 48000 |
|
7000 |
6 |
7000 * 6 = 42000 |
|
8000 |
4 |
8000 * 4 = 32000 |
|
9000 |
3 |
9000 * 3 = 27000 |
|
10000 |
1 |
10000 * 1 = 10000 |
|
Total |
60 |
305000 |
Mean = (305000)/60 = 5083.33.
Thus, the required mean salary = ₹ 5083.33
问题6.举一个例子说明
(i)均值是集中趋势的适当度量。
(ii)平均值不是中央趋势的适当度量，但中位数是中央趋势的适当度量。
解决方案：
(i) Mean height of family members where all are of approximately the same height. The entries in this case will be close to each other. Therefore, the mean will be calculated as an appropriate measure of central tendency.
(ii) Median weight of a pen, a book, a Cotton Pack, a matchbox, and a Table.