answer:You've already got a good grasp of the definitions. Let me provide a simple example to illustrate each concept: Imagine you have a set of exam scores from 5 students: 70, 80, 90, 80, 75. - The **mean** is the average of these scores. To calculate the mean, add up all the scores (70 + 80 + 90 + 80 + 75 = 395) and divide by the number of scores (5). The mean is 395 / 5 = 79. - The **median** is the middle value. First, arrange the scores in order: 70, 75, 80, 80, 90. Since there are an odd number of scores, the middle value is the third score, which is 80. - The **mode** is the value that appears most often. In this case, the score 80 appears twice, which is more than any other score. Therefore, the mode is 80. In this example, the mean is 79, the median is 80, and the mode is 80. These three measures of central tendency can help you understand the distribution of your data, but they can also be different, as shown in this example.

answer:Percentiles and quartiles are measures used to divide a dataset into equal parts, helping you understand the distribution of the data. **Percentiles**: A percentile is a value below which a certain percentage of the data falls. For example, the 25th percentile is the value below which 25% of the data falls. **Quartiles**: Quartiles are a type of percentile that divides the data into four equal parts. The three main quartiles are: - Q1 (25th percentile): the value below which 25% of the data falls - Q2 (50th percentile or median): the value below which 50% of the data falls - Q3 (75th percentile): the value below which 75% of the data falls Using the list of numbers: 10, 12, 15, 18, 20, 24, 30, 32, 35, 40, let's calculate the quartiles: First, arrange the numbers in order (already done). Since there are 10 numbers, the positions of the quartiles are: - Q1 (25th percentile): between the 2nd and 3rd numbers (since 25% of 10 is 2.5) - Q2 (50th percentile or median): between the 5th and 6th numbers - Q3 (75th percentile): between the 7th and 8th numbers The values are: - Q1 (25th percentile): (12 + 15) / 2 = 13.5 - Q2 (50th percentile or median): (20 + 24) / 2 = 22 - Q3 (75th percentile): (30 + 32) / 2 = 31 These quartiles tell you that: - 25% of the numbers are below 13.5 - 50% of the numbers are below 22 (the median) - 75% of the numbers are below 31 This helps you understand the spread and distribution of the data.

answer:The fact that the mean amount of rainfall (30.8 cm) is greater than the median amount (28.4 cm) tells us that the distribution of rainfall amounts is likely **skewed to the right** or **positively skewed**. This means that there are some very high values of rainfall (i.e., heavy rainfall events) that are pulling the mean upwards, while the majority of the rainfall amounts are actually lower, closer to the median. In other words, the mean is being influenced by extreme values (heavy rainfall events), whereas the median is a better representation of the typical or middle value of rainfall amounts. This suggests that the region may experience occasional heavy rainfall events, but most of the time, the rainfall amounts are relatively lower. If the distribution were symmetrical, the mean and median would be close in value. The difference between the mean and median in this case suggests that the distribution is not symmetrical, and the extreme values are having a significant impact on the mean.

answer:To solve this, we look at the function f(x) = begin{cases} 0, & x=0 x- frac {1}{x}, & xneq 0 end{cases}. It is clear that when x=0, f(x)=0. Setting f(x)=x- frac {1}{x}=0, we find that x=1 or x=-1. Therefore, the function f(x) has three zeros, namely x=0, x=1, and x=-1. Thus, the answer is boxed{3}. By using the definition of the zeros of a function, we can conclude the number of zeros of the function. This question mainly examines the application of piecewise functions, the definition of the zeros of a function, and finding the zeros of a function, which is a basic question.