The data show the number of children U.S. Presidents through...

The data show the number of children U.S. Presidents through Obama, had. Construct an ungrouped frequency distribution and find the mean and modal class. $\begin{array}{llllllllll}{0} & {5} & {6} & {0} & {3} & {4} & {1} & {4} & {10} & {8} \\ {7} & {0} & {6} & {1} & {0} & {3} & {4} & {5} & {4} & {8} \\ {7} & {3} & {5} & {2} & {1} & {2} & {1} & {5} & {3} & {3} \\ {0} & {0} & {2} & {2} & {6} & {1} & {2} & {3} & {2} & {2} \\ {4} & {4} & {2} & {6} & {1} & {2} & {2} & {}\end{array}$

The data show the number of children U.S. Presidents through Obama, had. Construct an ungrouped frequency distribution and find the mean and modal class.
$\begin{array}{llllllllll}{0} & {5} & {6} & {0} & {3} & {4} & {1} & {4} & {10} & {8} \\ {7} & {0} & {6} & {1} & {0} & {3} & {4} & {5} & {4} & {8} \\ {7} & {3} & {5} & {2} & {1} & {2} & {1} & {5} & {3} & {3} \\ {0} & {0} & {2} & {2} & {6} & {1} & {2} & {3} & {2} & {2} \\ {4} & {4} & {2} & {6} & {1} & {2} & {2} & {}\end{array}$

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Key Concepts

Ungrouped Frequency Distribution

An ungrouped frequency distribution is a table that lists each unique value from a dataset along with its frequency or count. This format retains the individual data values rather than aggregating them into intervals, making it particularly useful for small datasets or when exact data values are important.

Arithmetic Mean

The arithmetic mean, often simply called the mean, is a measure of central tendency calculated by summing all the data values and then dividing by the number of observations. It provides a single representative value that reflects the overall level of the dataset.

Modal Class

The modal class is the category or interval in a frequency distribution that has the highest frequency, meaning it occurs more than any other. In the context of ungrouped data, this concept relates to the mode, which is the most frequently occurring value in the dataset.

Transcript

00:01 In this problem, we're given a data set for the number of children of u .s.

00:06 Presidents up until president obama.

00:08 And we're asked to create an ungrouped frequency distribution.

00:14 So we look at the least number of children to the most number of children, and that's going to determine our classes.

00:21 So we'll have zero to ten for our class.

00:25 And then for frequency, we just need to go through and count.

00:29 So for zero children, there were six presidents, six presidents had one child, 10 presidents had two children, six presidents had three, six presidents had four, four presidents had five children, four presidents had six children, two presidents had seven, two presidents had eight, no presidents had nine children, and there was one president with an impressive of 10 children.

00:57 So here what we want to do is add up our frequency.

01:02 So here we will add 6 plus 6 plus 10 plus 6 plus 4 plus 4 plus 2 plus 2 plus 1.

01:12 And we will get a total of 47.

01:15 So we're looking at the first 47 presidents.

01:19 So then for the last column it's going to be the class times the frequency.

01:25 So for that first group, it would look like 0 times 6.

01:33 So 0 times 6 will be 0.

01:37 Then 1 times 6 will give us 6...