Question

find the mean, median, and mode of the following data: (round to 1 decimal place as needed) 35, 17, 20, 31, 17, 27, 33, 17, 27, 18 mean = median = mode =

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, $n = 10$, and $\sum_{i=1}^{10}x_{i}=35 + 17+20 + 31+17+27+33+17+27+18=242$. So, $\bar{x}=\frac{242}{10}=24.2$.

Step2: Calculate the median

First, arrange the data in ascending order: $17,17,17,17,18,20,27,27,31,35$. Since $n = 10$ (an even number), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data - points. $\frac{n}{2}=5$ and $\frac{n}{2}+1 = 6$. The 5th value is $18$ and the 6th value is $20$. So, the median $M=\frac{18 + 20}{2}=19.0$.

Step3: Calculate the mode

The mode is the data - point that appears most frequently. In the data set $17,17,17,17,18,20,27,27,31,35$, the number $17$ appears $4$ times, more frequently than any other number. So, the mode is $17$.

Answer:

Mean = $24.2$
Median = $19.0$
Mode = $17$