Question

look at this set of 7 numbers:
89 65 86 14 42 61 14
which value would change the most if the number 42 replaced one of the 14s in the set?
mean median mode
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Explanation:

Step1: Calculate original mean, median and mode

• Mean:

Original sum \(S_1=89 + 65+86 + 14+42+61+14=371\). Mean \(\bar{x}_1=\frac{371}{7}\approx53\).

• Median:

Sort the numbers: \(14,14,42,61,65,86,89\). Median \(m_1 = 61\).

• Mode:

Mode \(Mo_1=14\) (appears twice).

Step2: Calculate new mean, median and mode after replacement

• Mean:

New sum \(S_2=89 + 65+86 + 42+42+61+14=399\). Mean \(\bar{x}_2=\frac{399}{7}=57\).

• Median:

Sort the new - set: \(14,42,42,61,65,86,89\). Median \(m_2 = 61\).

• Mode:

Mode \(Mo_2 = 42\) (appears twice).

Step3: Calculate the changes

• Change in mean: \(\Delta\bar{x}=57 - 53 = 4\).
• Change in median: \(\Delta m=61 - 61=0\).
• Change in mode: \(\Delta Mo=42 - 14 = 28\).

Answer:

mode