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Video Transcript (0:05) The four major components of statistics and data analysis that show up on standardized tests are the mean, median, mode, and range. (0:13) You may have heard of these concepts as part of an algebra class, but all of these measures are attempting to describe a set of data in some way. When you take a statistics class, this group of values will often be called the measures of central tendency, which simply means that they try to measure where the center of our data is! (0:33) The mean is simply the arithmetic average of all of the values in a data set. An easy way to remember this is that a teacher who is mean will average in all of your grades, even the bad ones! (0:46) This is a fairly straightforward calculation, since you simply add up all of the values in the data set and then divide by the number of values you had. (0:56) For instance, suppose that you get a 90%, 80%, 85%, 95%, and then 100% on your class tests. (1:06) To find your mean score on these tests, simply add up all of the values to find that 90 + 80 + 85 + 95 + 100 = 450. (1:18) Divide this by the number of scores you had, which is 5 total tests, and you have earned an average of 450/5 = 90%. (1:30) The median is another measure of central tendency, but it is more true to measuring the actual center of the data. To find the median of a data set, you must order the data from smallest to largest and then cross off the largest and smallest value until you find the center. (1:47) An easy way to remember the median is to consider the median of a road! The median is also the middle part of a road that separates the two halves of a road and sometimes is made of concrete and has trees. (2:02) It is important to note that this works nicely when you have an odd number of values, but if you have an even number of values, there won’t be an exact middle value! The solution to this is to average your middle two values. (2:15) For example, suppose that you ran 4 laps around a track. Your time for each lap was 50 seconds, 45 seconds, 30 seconds, and 55 seconds. (2:28) To find the median lap time, we would need to first order this data from smallest to largest to find: 30, 45, 50, 55 (2:39) Then, we must cross off the smallest and largest value simultaneously. 30, 45, 50, 55 (2:44) Since there are two middle values, we take the average of them to find that the median is (45 + 50)/2 = 47.5. (2:55) Thus, we know that the median lap time was 47.5 seconds! (3:00) The mode of a data set is one of the easiest to calculate and the easiest to remember. The mode is the value that occurs most often. Notice how I emphasized the letters “mo.” This is because the word most and the word mode both begin with the same two letters. (3:18) A student could conduct an experiment on tomato plant growth to see how quickly different types of tomato plants grow. After observing the height of the plants, the student could have a data set that looks like {12, 10, 13, 11, 9, 7, 15, 8, 9, 9, 10}, where each plant’s height is measured in inches. (3:39) To calculate the mode, we simply look through the data set and count how many times each value appears. As we read our data set from left to right, we see that 9 occurs 3 times and 10 occurs 2 times, while all of the other numbers appear only once. (3:55) Therefore, 9 is the mode of our data! Note that if we had a tie between two numbers occurring the same amount, we can actually have two modes in our data set. (4:07) Finally, the range of a data set is the difference between the largest and smallest values in the data set. The most common errors when calculating range come from students who jump into the process of calculating it too quickly and use other values besides the largest and smallest. (4:25) For instance, a town in Alaska could measure its daily high temperatures over a week in January and find that the temperatures are as follows: {-4, 5, 1, -2, -5, 8, 7}, where each number represents the temperature in degrees Fahrenheit. (4:44) To find the range of temperatures for the week, we must find the lowest temperature and the highest temperature. (4:51) The lowest temperature is -5 degrees Fahrenheit, very cold! (4:56) The highest temperature is 8 degrees Fahrenheit, which is not much warmer! (5:01) To calculate the range, we subtract the lowest value from the highest value to find that the temperatures ranged a total of 8 - (-5) = 8 + 5 = 13 degrees Fahrenheit throughout the week. (5:15) In all of the examples we’ve been presented with, notice how each one used a totally different measurement and a different scenario. This is because statistics and measures of central tendency are incredibly useful to almost every situation you find yourself in, whether that’s in the real world or just a math test!
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Data, data, data! Most jobs and businesses rely on analyzed data to perform well in the working world, including the ERB. How else do you think the ERB determines Scaled Scores, Percentile Ranks, and Stanines for your ISEE results? Since the beginning, even your grades in school have been analyzed to show you and your parents how well you have been performing in class. What you complete in class, such as homework, projects, quizzes, and tests, are given a specific weight and scored. Tests might count three times as much as a quiz, for instance. These scores are all averaged, or added together and then divided by the number of scores that were added, including the weights given to each type of score. This average is your grade point average (GPA), which indicates whether or not you move onto the next grade level and can determine where you go for high school or college! Mean, Median, Mode, Range, and Weighted Average are some of the most basic ways of analying data. Mean (Average) Weighted Average Median Mode Range Box and Whisker Plots Steam and Leaf Plots Scatter Plots Keep in Mind Practice Problems Answers to Practice Questions Mean = 5, median = 5.5, mode = 2, range = 11. 14 B Mean = 22.3, median = 20.5, mode = none, range = 38. B
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