which data set has a mean of 18, a median of 18, and a mode of 18?\n12, 13, 15, 18, 18, 18, 19, 21, 24…

Explanation:

Step1: Recall mean formula

Mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, median is middle - value (for odd $n$) or average of two middle - values (for even $n$), mode is the most frequent value.

Step2: Check first data - set

Data set: $12,13,15,18,18,18,19,21,24,26$. $n = 10$. $\sum_{i=1}^{10}x_{i}=12 + 13+15+18+18+18+19+21+24+26=184$. Mean $=\frac{184}{10}=18.4$. Median: $\frac{18 + 18}{2}=18$. Mode: $18$.

Step3: Check second data - set

Data set: $12,13,15,17,18,18,19,20,23,25$. $n = 10$. $\sum_{i = 1}^{10}x_{i}=12+13+15+17+18+18+19+20+23+25 = 170$. Mean $=\frac{170}{10}=17$. Median: $\frac{18 + 18}{2}=18$. Mode: $18$.

Step4: Check third data - set

Data set: $12,12,13,13,14,14,18,18,18,18$. $n = 10$. $\sum_{i=1}^{10}x_{i}=12\times2 + 13\times2+14\times2+18\times4=24 + 26+28+72 = 150$. Mean $=\frac{150}{10}=15$. Median: $\frac{14 + 18}{2}=16$. Mode: $18$.

Step5: Check fourth data - set

Data set: $11,13,14,19,19,20,21,23,25,28$. $n = 10$. $\sum_{i=1}^{10}x_{i}=11+13+14+19+19+20+21+23+25+28 = 193$. Mean $=\frac{193}{10}=19.3$. Median: $\frac{19 + 20}{2}=19.5$. Mode: $19$.

Step6: Calculate mean of second part

Data set: $18,36,24,36,30,36$. $n = 6$. $\sum_{i=1}^{6}x_{i}=18+36+24+36+30+36=180$. Mean $=\frac{180}{6}=30$.

Answer:

First question: None of the above. Second question: B. 30