Question

16)Calculate the mean, mode, and midrange from the frequency table given below. Estimate the median.ValueFrequency129136144157164To find Mean: x = ∑ x nMode: The mode is the number that appears the most in given data which is ____ since it is given three times.Mode =To find Midrange:Mid−range = Max(x) + Min(x)2

Answer 1

In our table, we have the following set of values for the frequency:

$\lbrace9,6,4,7,4\rbrace$

The mean of a dataset is the sum of all elements divided by the total amount of elements. The mean of our set is:

$\bar{x}=\frac{\sum_{i\mathop{=}1}^5x_i}{5}=\frac{9+6+4+7+4}{5}=\frac{30}{5}=6$

The mean of the frequency is equal to 6.

The mode is the number that appears the most in given data which is 4 since it is given two times.

To find the median we need to reorder our dataset in ascending order.

$\lbrace4,4,6,7,9\rbrace$

The median is the middle number in a sorted, ascending or descending, list of numbers. In our problem, the middle element is 6, therefore, the median is 6.

The maximum value of our dataset is 9 and the minimum value is 4, therefore, the midrange is:

$\frac{9+4}{2}=\frac{13}{2}=6.5$

The midrange of the dataset is 6.5.