Question

look at this set of 6 numbers: 59 53 61 59 65 81 which value would change the most if the number 63 were added to the set? mean median mode save answer

Explanation:

Step1: Calculate the original mean

The original set is \(53,59,59,61,65,81\).
The sum of the original set is \(53 + 59+59+61+65+81=378\).
The original mean is \(\frac{378}{6}=63\).

Step2: Calculate the new mean

After adding \(63\), the new set is \(53,59,59,61,63,65,81\).
The new sum is \(378 + 63=441\).
The new mean is \(\frac{441}{7}=63\).

Step3: Calculate the original median

For the original set (\(n = 6\), even), the median is the average of the \(3^{rd}\) and \(4^{th}\) values.
The \(3^{rd}\) value is \(59\), the \(4^{th}\) value is \(61\).
The original median is \(\frac{59 + 61}{2}=60\).

Step4: Calculate the new median

For the new set (\(n=7\), odd), the median is the \(4^{th}\) value.
The new set in order is \(53,59,59,61,63,65,81\), so the new median is \(61\).

Step5: Analyze the mode

The original mode is \(59\) (appears twice). After adding \(63\), the mode is still \(59\) (appears twice, and \(63\) appears once).

Answer:

median