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Module 1: Measures of Central Tendency: Mean, Median, Mode

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    The arithmetic mean, written as overline{x}, is the best measure of central tendency. It is the average of the entire set of observations.
    (The Greek letter, sigma, is used to denote summation.)
    The formula for the mean is overline{x} =frac{Sigma x}{n}, where Sigma x is the sum of the numbers and n is the total number of values being averaged.
     
    Example 1: Kiran received the following scores on his math tests during the first marking period: 87, 83, 91, 90, and 97. Find his average.
     
    Solution: overline{x} =frac{87+83+91+90+97}{5}=frac{448}{5} = 89.6
     
    Do you think the teacher should round this average to 90 and give Kiran an A for the marking period? Explain why.
     
    Example 2: The manager of a bicycle store recorded the following sales: March - 43 bikes, April - 40 bikes, May - 59 bikes, June - 70 bikes and July 97 bikes. How many bikes must he sell in August to average 68 bikes sales per month over this 6 month period of time?
     
    Solution: Let x represent the number of bikes that must be sold in August.
     
    Then, 68=frac{43+40+59+70+97+x}{6}
     
    68=frac{309 + x}{6}
     
    408=309+x
     
    99=x
     
    Therefore, the manager must sell 99 bikes in August.
     
    Properties of arithmetic mean
    The algebraic sum of the deviations of the individual values from their arithmetic mean is zero.
    If each observation is increased by a then the new mean is also increased by a.
    If each observation is decreased by a then the new mean is also decreased by a.
    If each observation is multiplied by a, then the new mean is also multiplied by a.
    If each observation is divided by a, then the new mean is also divided by a.
    Extreme values in the data affect the mean.