Question

find the mean, median, and mode of the data set: 4, 7, 11, 5, 14, 9, 7, 12. press each hotspot. label the corresponding number below with the requested value. press to hear a reminder or hint for this

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data - points and $n$ is the number of data - points. Here, $n = 8$, and $\sum_{i=1}^{8}x_{i}=4 + 7+11 + 5+14 + 9+7+12=79$. So, $\bar{x}=\frac{79}{8}=9.875$.

Step2: Calculate the median

First, arrange the data in ascending order: $4,5,7,7,9,11,12,14$. Since $n = 8$ (an even number), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data - points. $\frac{n}{2}=4$ and $\frac{n}{2}+1 = 5$. The 4th value is 7 and the 5th value is 9. So, the median $=\frac{7 + 9}{2}=8$.

Step3: Calculate the mode

The mode is the data - point that appears most frequently. In the data set $4,7,11,5,14,9,7,12$, the number 7 appears twice, and all other numbers appear only once. So, the mode is 7.

Answer:

Mean: $9.875$, Median: $8$, Mode: $7$