Below are the percentages of the population over 25 years of...

Below are the percentages of the population over 25 years of age who have completed 4 years of college or more for the 50 states and the District of Columbia. Find the mean and modal class. Percentage$\quad$ Frequency $\begin{array}{ll}{15.2-19.6} & {3} \\ {19.7-24.1} & {15} \\ {24.2-28.6} & {19} \\ {28.7-33.1} & {6} \\ {33.2-37.6} & {7} \\ {37.7-42.1} & {0} \\ {42.2-46.6} & {1}\end{array}$

Below are the percentages of the population over 25 years of age who have completed 4 years of college or more for the 50 states and the District of Columbia. Find the mean and modal class.
Percentage$\quad$ Frequency
$\begin{array}{ll}{15.2-19.6} & {3} \\ {19.7-24.1} & {15} \\ {24.2-28.6} & {19} \\ {28.7-33.1} & {6} \\ {33.2-37.6} & {7} \\ {37.7-42.1} & {0} \\ {42.2-46.6} & {1}\end{array}$

Key Concepts

Arithmetic Mean for Grouped Data

The arithmetic mean for grouped data is estimated by assuming that all data points in a class are concentrated at the midpoint of that interval. To calculate it, you multiply each class's midpoint by its frequency, add these products together, and then divide by the total number of observations.

Modal Class

The modal class is the interval in a frequency distribution that contains the highest frequency of observations. It gives an indication of where the bulk of the data lies and serves as a measure of central tendency, especially when the mode cannot be directly computed from individual values.

Grouped Data

Grouped data refers to data that has been organized into intervals or classes rather than listed individually. This arrangement is particularly useful when dealing with large datasets, as it simplifies the data and makes it easier to analyze overall patterns and trends.

Frequency Distribution

A frequency distribution is a table that displays the number of observations within each given interval or class of a dataset. This tool helps in understanding how data is spread out and is essential for further statistical analysis, such as finding measures of central tendency.

Transcript

00:01 In this problem, we're looking at the population greater than 25 years old with four or more years of college experience.

00:07 And the first class we're given is 15 .2 % to 19 .6 % with a frequency of three.

00:17 And then our classes go all the way up to the last class being 42 .2 % to 56 .6%.

00:26 And then here are the frequencies for each of those classes.

00:30 The very first thing we want to do when we're trying to find the mean and modal class of a grouped distribution is add up all of our frequencies.

00:43 So we'll add 3 plus 15 plus 19 plus 6 plus 7 plus 1 for a total of 51.

00:51 Then we want to calculate the midpoint for each of our classes.

00:55 So to do the midpoint, we'll take the average of the lower bound and the upper bound for the class.

01:02 So we'll do 15 .2 plus 19 .6 divided by 2.

01:10 And here we'll see that our midpoint is 17 .4.

01:22 Then for the second class, following the same guidelines here, 19 .7 plus 24 .1.

01:31 Divided by 2, we will get 21 .9.

01:37 So then we'll continue that same process, and the third midpoint for the third class will be 26 .4.

01:47 For the next class, 30 .9, then 35 .4, then 39 .9.

01:58 And lastly, we will get a midpoint of 44 .4.

02:06 Then what we want to do is take our frequency column and multiply it by the midpoint.

02:13 So for this first class, that would look like 3 times 17 .4...

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