Question

look at this set of 8 numbers:
39 49 80 34 13 78 80 19
which value would change the most if the number 59 replaced the number 19 in the set?
mean median mode
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Explanation:

Step1: Calculate the original mean

The original set is \(39,49,80,34,13,78,80,19\).
The sum of the original set is \(39 + 49+80+34+13+78+80+19=\sum_{i = 1}^{8}x_{i}=392\).
The mean \(\bar{x}_{1}=\frac{392}{8}=49\).

Step2: Calculate the new mean

The new set is \(39,49,80,34,13,78,80,59\).
The sum of the new set is \(39 + 49+80+34+13+78+80+59=\sum_{i = 1}^{8}y_{i}=432\).
The new mean \(\bar{x}_{2}=\frac{432}{8}=54\).

Step3: Calculate the original median

Sort the original set: \(13,19,34,39,49,78,80,80\).
The median \(M_{1}=\frac{39 + 49}{2}=44\).

Step4: Calculate the new median

Sort the new set: \(13,34,39,49,59,78,80,80\).
The median \(M_{2}=\frac{49+59}{2}=54\).

Step5: Analyze the mode

The mode of the original set is \(80\) (appears twice).
The mode of the new set is still \(80\) (appears twice).

The change in mean is \(54 - 49=5\).
The change in median is \(54 - 44 = 10\).

Answer:

mean