Group data question: What is the mean number of calories in a drink? The Standard deviation? and the variance?

prc85040 asked:


Three drinks have 37.5 calories. Four drinks have 112.5 calories. Eight drinks have 187.5 calories. Seven drinks have 262.5 calories. Nine drinks have 337.5 calories. Five drinks have 412.5 calories. Four drinks have 487.5 calories. Two drinks have 562.5 calories.

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One Response to “Group data question: What is the mean number of calories in a drink? The Standard deviation? and the variance?”

  1. hpage on August 11th, 2009 at 1:11 pm

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    mean: average

    3*37.5=112.5 cal
    4*112.5=450
    8*187.5=1500
    7*262.5=1837.5
    9*337.5=3037.5
    5*412.5=2062.5
    4*487.5=1950
    2*562.5=1125 cal

    add up total amount of drinks and number of total calories

    so, N=42 drinks
    total calories for all drinks =12075 cal
    mean = 12075/42 = 287.5 cal in a drink

    To find the variance, you need to find the sum of squares (SS)

    take each drink and subtract the mean just found, then square this value, once all are found, add all up to find SS
    So, since mean=287.5 cal, then

    37.5-287.5=-250, then square this, -250^2=62500, but there are 3 drinks that have 37.5cal so, 62500*3=187500, repeat
    112.5-287.5=-175, -175^2=30625, *4=122500
    187.5-287.5=-100, 10000, *8=80000
    262.5-287.5=-25, 625, *7=4375
    337.5-287.5=50, 2500, *9=22500
    412.5-287.5=125, 15625, *5=78125
    487.5-287.5=200, 40000, *4=160000
    562.5-287.5=275, 75625, *2=151250

    Now, add up all the big numbers at the end of each line
    I get 806250=SS

    variance=SS/N = 806250/42 = 19196.428

    standard deviation is the square root of variance
    sqrt of 19196.428 = 138.55 : std dev

    hope you got all of this… :)

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