Sample Midterm 1 - key

# Sample Midterm 1 - key - Solutions to 1st Midterm...

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Solutions to 1 st Midterm Examination 1) a) The histogram that corresponds to this sample is: b) To find the mean, we must use the formula µ X = ( k = 1 K f k m k )/N , where m k is the midpoint of the k th class, f k is the number of observations in the k th class, and N is the number of observations. In this case, µ X = ((4.5)*2700+(10.5)*3012+(13)*16000+(15.5)*15366+(21.5)*10978)/48056 = 725976/48056 = 15.1069 years of schooling . c) To do a box-and-whiskers plot, we must first determine the median and the first and third quartiles. Since there are 48056 observations, the first quartile is the (48056+1)/4 = 12014.25 th observation. This observation is 6302.25 th observation in the 12 to 14 interval. Using the formula for the value of the observation in an interval, we have Value of 6302.25 th observation = 12 + (6302.25-0.5)(2/16000) = 12.7877 . So, the first quartile is 12.7877 . The median is the 2(48056+1)/4 = 24028.5 th observations. This observation is the 2316.5 th observation

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in the 14-17 interval. So, the median is given by Value of 2316.5 th observation = 14 + (2316.5-0.5)(3/15366) = 14.4522 .
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