There are several ways to measure steepness. The gradient is a measure of the steepness of line. Take the average of the x-coordinates and the average of the y-coordinates. The midpoint of an interval with endpoints P( x 1, y 1) and Q( x 2, y 2) is. Hence the x-coordinate of M is the average of x 1 and x 2, and y-coordinate of M is the average of y 1 and y 2. Triangles PMS and MQT are congruent triangles (AAS), and so PS = MT and MS = QT. ![]() Suppose that P( x 1, y 1) and Q( x 2, y 2)are two points and let M( x, y) be the midpoint. We can find a formula for the midpoint of any interval. Thus the coordinates of the midpoint M are (3, 5). The y coordinate of M is the average of 2 and 8. Hence the x-coordinate of M is the average of 1 and 5. Triangles AMS and MBT are congruent triangles (AAS), and so AS = MT and MS = BT. When the interval is not parallel to one of the axes we take the average of the x-coordinate and the y-coordinate. Note: 4 is the average of 1 and 7, that is, 4 =. Midpoint is at (4, 2), since 4 is halfway Note that ( x 2 − x 1) 2 is the same as ( x 1 − x 1) 2 and therefore it doesn’t matter whether we go from P to Q or from Q to P − the result is the same.įind the coordinates of the midpoint of the line interval AB, given:Ī A(1, 2) and B(7, 2) b A(1, −2) and B(1, 3) PX = x 2 − x 1 or x 1 − x 2 and QX = y 2 − y 1 or y 1 − y 2 Suppose that P( x 1, y 1) and Q( x 2, y 2) are two points.įorm the right-angled triangle PQX, where X is the point ( x 2, y 1), We can obtain a formula for the length of any interval. The distance between the points A(1, 2) and B(4, 6) is calculated below. Pythagoras’ theorem is used to calculate the distance between two points when the line interval between them is neither vertical nor horizontal. The example above considered the special cases when the line interval AB is either horizontal or vertical. The difference of the y-coordinates of the The highest number is 17.Find the distance between the following pairs of points.Ī A(1, 2) and B(4, 2) b A(1, −2) and B(1, 3) It can help to put the numbers in order so we don't miss anything: 4, 4, 7, 8, 9, 14, 17įour appears twice and the rest of the numbers only appear once. Remember the mode is the number that appears the most. The mean is 9.įirst put the numbers in order: 4, 4, 7, 8, 9, 14, 17 Then divide 63 by the total number of data points, 7, and you get 9. The range is 25.Įxample problem finding mean, median, mode and range:įind the mean, median, mode and range of the following data set:įirst add the numbers up: 9+4+17+4+7+8+14 = 63 Then the rest of the scores don't matter for range. Let's say your best score all year was a 100 and your worst was a 75. Range - Range is the difference between the lowest number and the highest number. It's also the meanest because it take the most math to figure it out. Here are some tricks to help you remember: They all start with the letter M, so it can be hard to remember which is which sometimes. If all the numbers appear the same number of times, then the data set has no modes. If there are more than 2 then the data would be called multimodal. If there are two numbers that appear most often (and the same number of times) then the data has two modes. There are a few tricks to remember about mode: Mode - The mode is the number that appears the most. If there is an even number of data points, then you need to pick the two middle numbers, add them together, and divide by two. If there is an odd number of data points, then you will have just one middle number. To figure out the median you put all the numbers in order (highest to lowest or lowest to highest) and then pick the middle number. Median - The median is the middle number of the data set. This would give you the mean of the data. For example, if you have 12 numbers, you add them up and divide by 12. You can figure out the mean by adding up all the numbers in the data and then dividing by the number of numbers. Mean - When people say "average" they usually are talking about the mean. ![]() Together with range, they help describe the data. Mean, median, and mode are all types of averages. The term "average" is used a lot with data sets. When you get a big set of data there are all sorts of ways to mathematically describe the data.
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