Unit #4: Statistics Lesson #1: Mean, Median, Mode, & Standard Deviation
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1 Algebra I Name Unit #4: Statistics Lesson #1: Mean, Median, Mode, & Standard Deviation Period Date Before we jump into our last unit, we need to review some important definitions about data. Looking at a bunch of data can be confusing. There are some calculations we can do that provides us a better understanding of the data we are given. The mean of a set of data is another way of asking for the average. To find the mean of a set of data, you simply up all the data points and by how many data points you have. The median is the number that is in the of all the data points. To find median, you first MUST put all the data points in order from to. Work your way to the middle of the list and you will find the median. If there is an odd number of data points, the median is the number in the middle. If there is an even number of data points, you won t have just one number in the middle. Take the two numbers in the middle of your list and average them together. The mode is the data point that occurs the. It is possible that you can have more than one mode. It is possible that you do not have a mode. Standard deviation is a way to measure how spread out your data is. If the standard deviation is low, that means your data is not really spread out much. All your data points are close together. If the standard deviation is higher, that means your data is much more spread out. The range of a set of data is the difference between the and values in the set. To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set. Data sets can be skewed. When a bunch of the data points appear to be clustered on either the left side or the right side of your graph, the data is skewed.
2 Data doesn t always have to be skewed though! Here is an example of data that is not skewed. This is said to be evenly spread. Ex #1: Is this data skewed or evenly spread? Explain how you know? Ex #2: Find the mean, median, and mode of the following set of data Mean: Median: Mode: Is there a data point that kinda looks out of place? Which one?. When looking at data, sometimes there might be a number that is way higher or way lower than the rest. This point is called an outlier, because it lies way out from the rest of the data.
3 Ex #3: Below are test scores from our last math test. Find the mean, median, and mode for the following set of data. Identify any outliers. Mean: Median: Mode: Outlier(s): NOW, the good thing is that your calculator can determine the mean, median, and standard deviation pretty easily.if you know how to do it. Soooooo, lets learn how to do it. STEP 1: Press STAT and select EDIT STEP 2: If there are numbers already in your list, move your cursor to the top of each list, press CLEAR, then ENTER. STEP 3: Enter all your data into L1. STEP 4: Double check that you entered it all in correctly. STEP 5: Press STAT, go to CALC, and choose the 1: 1-Var Stats. Press ENTER. STEP 6: Move your cursor down to Calculate and press ENTER. Whoa. That s a lot of numbers. Here is what s important. x = the mean (average) σx = the standard deviation n = how many numbers you typed in minx = the smallest number (minimum) Q1 = the first quartile Med = the median Q3 = the third quartile maxx = the largest number (maximum) All we care about now is the mean and the standard deviation. We ll deal with the other numbers tomorrow.
4 Ex #4: The two sets of data below represent the number of runs scored by two different youth baseball teams over the course of a season. Team A: 4, 8, 5, 12, 3, 9, 5, 2 Team B: 5, 9, 11, 4, 6, 11, 2, 7 Which set of statements about the mean and standard deviation is true? (a) (b) (c) (d) mean A < mean B standard deviation A > standard deviation B mean A > mean B standard deviation A < standard deviation B mean A < mean B standard deviation A < standard deviation B mean A > mean B standard deviation A > standard deviation B Ex #5: The table below shows the annual salaries for the 24 members of a professional sports team in terms of millions of dollars. The team signs an additional player to a contract worth 10 million dollars per year. Which statement about the median and mean is true? (a) (b) (c) (d) Both will increase. Only the median will increase Only the mean will increase Neither will change
5 Ex #6: The heights, in inches, of 12 students are listed below. 61,67,72,62,65,59,60,79,60,61,64,63 Which statement best describes the spread of these data? (1) The set of data is evenly spread (2) The median of the data is 59.5 (3) The set of data is skewed because 59 is the only value below 60 (4) 79 is an outlier, which would affect the standard deviation of these data. Ex #7: The 15 members of the French Club sold candy bars to help fund their trip to Quebec. The table below shows the number of candy bars each member sold. Number of Candy Bars Sold When referring to the data, which statement is false? (1) The mode is the best measure of central tendency for the data (2) The data have two outliers (3) The median is 53 (4) The range is 120
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