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Math Help - Using stem and leaf, mean and standard deviation to choose the better variety?

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    Using stem and leaf, mean and standard deviation to choose the better variety?

    Hi, I have a question where I'm asked to compare two varieties of corn (A and B) and decide which one the farmer should plant in the future. A grid was given which showed 32 equally sized plots with Variety A planted randomly in 16 plots and Variety B in the remaining. The yield in kg was given for each plot. I made a back to back stem and leaf plot which looks like this:



    I then used my TI calculator to determine the mean yield and standard deviation for both types. I got:

    Variety A: mean yield = 11.2 kg and standard deviation = 0.27 kg
    Variety B: mean yield = 10.09 kg and standard deviation = 0.54 kg

    I am not sure what I should say and discuss in my justification for which Variety is better. I think it's Type A but I have no idea what I should be saying to justify why using these answers (and how standard deviation is used to justify this). I also need to suggest why the plots for Variety A were randomly selected.

    Thanks for your help!
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  2. #2
    Member garymarkhov's Avatar
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    Quote Originally Posted by bemypenguinxx View Post
    Hi, I have a question where I'm asked to compare two varieties of corn (A and B) and decide which one the farmer should plant in the future. A grid was given which showed 32 equally sized plots with Variety A planted randomly in 16 plots and Variety B in the remaining. The yield in kg was given for each plot. I made a back to back stem and leaf plot which looks like this:



    I then used my TI calculator to determine the mean yield and standard deviation for both types. I got:

    Variety A: mean yield = 11.2 kg and standard deviation = 0.27 kg
    Variety B: mean yield = 10.09 kg and standard deviation = 0.54 kg

    I am not sure what I should say and discuss in my justification for which Variety is better. I think it's Type A but I have no idea what I should be saying to justify why using these answers (and how standard deviation is used to justify this). I also need to suggest why the plots for Variety A were randomly selected.

    Thanks for your help!
    Perhaps it's me, but based on the means you've reported, I think you may have made some mistakes in composing your stem and leaf plot. Let's take the last row as an example: you should put a 1 in the stem column and two 1's in the right leaf column if you want to show that there were two instances of Type B producing a yield of 11kg.

    In any case, once you've found your mean and standard deviations, you can make a judgment about which variety is better. All else equal, the farmer would probably prefer the variety that has a higher mean yield (more is better!). Also all else equal, the farmer would probably prefer the variety that has an output with the lowest standard deviation (because he prefers to have a crop that is predictable, rather than one that varies a lot).

    So if one variety has the highest mean AND the lowest standard deviation, the farmer would clearly prefer that variety. If one variety has the highest mean while the other variety has the lowest standard deviation, it's harder to know what the farmer would want until you know whether he is a risk-loving guy or whether he likes to play it safe.

    Hope that helps!
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