Data Set: 24, 24, 56, 37, 40, 27, 33, 30, 43, 10, 49

raubsjosh

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24, 24, 56, 37, 40, 27, 33, 30, 43, 10, 49
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Let's include one more data point in the data set. Suppose this new data value lies between the values 10 and 56, inclusively.
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[FONT=&quot]-Find the smallest possible value of the mean of the new data set: ???
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[FONT=&quot]-Find the largest possible value of the mean of the new data set: ???
[/FONT]
[FONT=&quot]-Find the smallest possible value of the median of the new data set: ???
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[FONT=Helvetica Neue, Helvetica, Arial, sans-serif]-Find the largest possible value of the median of the new data set: ???[/FONT]


[FONT=Helvetica Neue, Helvetica, Arial, sans-serif]I need help finding these new values [/FONT]
 
24, 24, 56, 37, 40, 27, 33, 30, 43, 10, 49

Let's include one more data point in the data set. Suppose this new data value lies between the values 10 and 56, inclusively.
a. Find the smallest possible value of the mean of the new data set: ???
b. Find the largest possible value of the mean of the new data set: ???
c. Find the smallest possible value of the median of the new data set: ???
d. Find the largest possible value of the median of the new data set: ???

I need help finding these new values
Okay; where are you stuck? For instance, you started by finding the sum of the initial values, knowing that the average will involve that sum (then divided by twelve, after adding one more value). You looked at the conditions on the new value for part (a), noted that it must be the smallest possible to give the smallest possible new average, and... then what?

For part (b), you used the same reasoning, and... then what?

For part (c), you listed the original values in numerical order (which is always necessary when considering the median), noted the location of the median of the original values, and... then what? Same question for part (d).

Please be complete, or specify that you first need lesson instruction on "means" and "medians". Thank you! ;)
 
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