5. find the mean, median and mode of the following data set. 29, 14, 80, 59, 78, 30, 59, 69, 55, 85, 50…

Explanation:

Step1: Calculate the mean

First, sum all data values: $29 + 14+80 + 59+78+30+59+69+55+85+50=618$. There are $n = 11$ data - points. The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}=\frac{618}{11}\approx56.18$.

Step2: Calculate the median

Arrange the data in ascending order: $14,29,30,50,55,59,59,69,78,80,85$. Since $n = 11$ (an odd number), the median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{11+1}{2}=6$-th value, which is $59$.

Step3: Calculate the mode

The mode is the value that appears most frequently in the data - set. The number $59$ appears twice, and all other numbers appear only once, so the mode is $59$.

Answer:

Mean: $\approx56.18$ Median: $59$ Mode: $59$