6. given the data below: 61, 62, 55, 68, 57, 61 a) find the mean, median, mode, and range.

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, $n = 6$, and $\sum_{i=1}^{6}x_{i}=61 + 62+55 + 68+57+61=364$. So, $\bar{x}=\frac{364}{6}=\frac{182}{3}\approx60.67$.

Step2: Calculate the median

First, order the data: $55,57,61,61,62,68$. Since $n = 6$ (an even number), the median is the average of the two middle - values. The two middle - values are the 3rd and 4th ordered values. So, median $=\frac{61 + 61}{2}=61$.

Step3: Calculate the mode

The mode is the value that appears most frequently in the data - set. Here, 61 appears twice, and all other values appear once. So, the mode is 61.

Step4: Calculate the range

The range is the difference between the maximum and minimum values in the data - set. The maximum value is 68 and the minimum value is 55. So, the range is $68−55 = 13$.

Answer:

Mean: $\frac{182}{3}\approx60.67$, Median: 61, Mode: 61, Range: 13