Question

which data set has a mean of 18, a median of 18, and a mode of 18?
12, 13, 15, 18, 18, 18, 19, 21, 24, 26
12, 13, 15, 17, 18, 18, 19, 20, 23, 25
12, 12, 13, 13, 14, 14, 18, 18, 18, 18
11, 13, 14, 19, 19, 20, 21, 23, 25, 28
question #8
find the mean of the data set: 18, 36, 24, 36, 30 and 36
27
30
36
26

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