The data show the maximum wind speeds for a sample of 40...

The data show the maximum wind speeds for a sample of 40 states. Find the mean and modal class for the data. Class boundaries $\quad$Frequency $\begin{array}{ll}{47.5-54.5} & {3} \\ {54.5-61.5} & {2} \\ {61.5-68.5} & {9} \\ {68.5-75.5} & {13} \\ {75.5-82.5} & {8} \\ {82.5-89.5} & {3} \\ {89.5-96.5} & {2}\end{array}$

The data show the maximum wind speeds for a sample of 40 states. Find the mean and modal class for the data.
Class boundaries $\quad$Frequency
$\begin{array}{ll}{47.5-54.5} & {3} \\ {54.5-61.5} & {2} \\ {61.5-68.5} & {9} \\ {68.5-75.5} & {13} \\ {75.5-82.5} & {8} \\ {82.5-89.5} & {3} \\ {89.5-96.5} & {2}\end{array}$

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Key Concepts

Modal Class

The modal class is the class interval that has the highest frequency of observations. It represents the range where the bulk of the data is concentrated, and is considered an indicator of the most common or typical value in the distribution.

Grouped Data

Grouped data refers to data that is organized into intervals or classes rather than listed individually. This method is used to condense large data sets into a more manageable form, making it easier to identify trends, central tendencies, and dispersion.

Mean for Grouped Data

The mean for grouped data is an estimated average computed by multiplying the midpoint of each class by its frequency, summing these products, and dividing by the total number of data points. This method accounts for the distribution of observations across the defined intervals.

Class Midpoint

The class midpoint, also known as the class mark, is the value found by averaging the lower and upper boundaries (or limits) of a class interval. It serves as a representative value for all data points within that interval when calculating estimates such as the mean.

Transcript

00:01 In this problem, we're looking at data for the max wind speeds for 40 different states.

00:07 And we're given all of the class and frequency for this.

00:12 So the very first class is 47 .5 to 54 .5.

00:18 And the frequency is three.

00:21 And then we continue with our classes until we get to 89 .5 to 96 .5.

00:28 And then we see the full frequency distribution here.

00:33 So first what we want to do is add up our total number of frequencies.

00:41 So we're going to add 3 plus 2 plus 9 plus 13 plus 8 plus 3 plus 2 to get a total of 40, which we should have already known that it would be 40, but we can just go through the process to double check.

00:57 So then we need to find the midpoint for the class.

01:01 So if we want to go through the process of finding the midpoint, we can take the average.

01:09 So we would do 47 .5 plus 54 .5 and divide it by 2 to go through the process of finding the midpoint, which for the first class is 51.

01:24 And then we would go through the same process for the second class.

01:28 So we would do 54 .5 plus 61 .5 divided by 2 and we will get 58.

01:34 So as we continue that process, the midpoints we would continue to get would be 65, 72, 79, 86, and 93.

01:52 So then the next thing we want to do is go through and multiply...

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