Question

which value can be added to the set without changing its mean? {4, 10, 14, 18, 22, 22}

Explanation:

Step1: Calculate the original mean

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). For the set \(\{4,10,14,18,22,22\}\), \(n = 6\) and \(\sum_{i=1}^{6}x_{i}=4 + 10+14+18+22+22=90\). So the original mean \(\bar{x}_{1}=\frac{90}{6}=15\).

Step2: Check each option

• Option 0:

Let \(n_{new}=7\), \(\sum_{new}=90 + 0=90\). The new mean \(\bar{x}_{new}=\frac{90}{7}\approx12.86
eq15\).

• Option 16:

Let \(n_{new}=7\), \(\sum_{new}=90 + 16=106\). The new mean \(\bar{x}_{new}=\frac{106}{7}\approx15.14
eq15\).

• Option 22:

Let \(n_{new}=7\), \(\sum_{new}=90+22 = 112\). The new mean \(\bar{x}_{new}=\frac{112}{7}=16
eq15\).

• Option 15:

Let \(n_{new}=7\), \(\sum_{new}=90 + 15=105\). The new mean \(\bar{x}_{new}=\frac{105}{7}=15\).

Answer:

15