Salaries of Governors Here are the salaries (in dollars) of...

Salaries of Governors Here are the salaries (in dollars) of the governors of 25 randomly selected states. Construct a grouped frequency distribution with 6 classes. $$ \begin{aligned} &\begin{array}{rrrrr} 112,895 & 117,312 & 140,533 & 110,000 & 115,331 \\ 95,000 & 177,500 & 120,303 & 139,590 & 150,000 \\ 173,987 & 130,000 & 133,821 & 144,269 & 142,542 \\ 150,000 & 145,885 & 105,000 & 93,600 & 166,891 \\ 130,273 & 70,000 & 113,834 & 117,817 & 137,092 \end{array}\\ &\text { Source: World Almanac } \end{aligned} $$

Salaries of Governors Here are the salaries (in dollars) of the governors of 25 randomly selected states. Construct a grouped frequency distribution with 6 classes.
$$
\begin{aligned}
&\begin{array}{rrrrr}
112,895 & 117,312 & 140,533 & 110,000 & 115,331 \\
95,000 & 177,500 & 120,303 & 139,590 & 150,000 \\
173,987 & 130,000 & 133,821 & 144,269 & 142,542 \\
150,000 & 145,885 & 105,000 & 93,600 & 166,891 \\
130,273 & 70,000 & 113,834 & 117,817 & 137,092
\end{array}\\
&\text { Source: World Almanac }
\end{aligned}
$$

Key Concepts

Grouped Frequency Distribution

A grouped frequency distribution is a method used to organize and summarize large sets of data by categorizing them into intervals or classes. This approach simplifies data analysis by converting raw data into frequency counts that show how many values fall within each interval.

Class Intervals

Class intervals are consecutive and non-overlapping ranges that divide the entire span of the data. They are designed to cover all possible values of the dataset and are typically chosen to maintain a uniform structure that facilitates comparison and analysis.

Range of Data

The range of data is the difference between the maximum and minimum values in a dataset. It represents the total span of the data and is crucial in determining the overall spread, which in turn helps in calculating an appropriate class width.

Class Width

Class width is the size of each interval in a grouped frequency distribution. It is usually determined by dividing the range of the data by the number of classes desired, ensuring that each class interval is equal in width, which simplifies the grouping process.

Frequency Count

Frequency count is the number of observations or data points that fall within each class interval. It provides a clear picture of the distribution of the data and is essential for identifying patterns, trends, or anomalies in the dataset.

Transcript

00:01 So you're supposed to take this data and put it into a frequency distribution with six classes.

00:08 So we know we're doing six classes.

00:14 So the first thing you will need to do is to determine the class width.

00:22 And to do that, we're going to first find the range of the data.

00:28 And then we're going to divide it by the number of classes, which in this case we've said was six.

00:37 So the range of the data is going to be the highest piece of data minus the lowest piece of data.

00:44 So i have placed all of my data into the graph and calculator.

00:49 So i'm going to hit stat and edit.

00:53 And you can see that all of the data has been entered.

00:56 And as i look, it looks like the lowest piece of data is 70 ,000, which is in position number 22 or cell number 22 in this case.

01:07 Case.

01:08 And the highest piece of data looks like it's in position number seven, which is 177 ,500.

01:19 So we're going to take 177 ,500, which is the highest minus the lowest, which is 70 ,000.

01:30 And that answer we will divide by six.

01:34 In doing so, we end up with 107 ,500 divided by six, which results in 17 ,916 .7, and you must always round up.

01:52 It doesn't matter how close you are to the number below.

01:56 So our class with is going to be 17 ,990.

02:08 17.

02:09 So now that we have our class width, we are ready to set up our distribution.

02:17 Now, our distribution is going to have four different columns.

02:24 We're going to have our class limits.

02:35 We're going to have our class boundaries.

02:48 You're going to have your tally and we'll have our frequency.

03:02 And to determine our class limits, the first thing you're going to do is you're going to start with the lowest piece of data.

03:10 And we said the lowest piece of data was 70 ,000.

03:16 And to that, we're going to take that 70 ,000, and we're going to add the class width to it.

03:25 And in doing so, we get 87 ,917.

03:31 Now that is not where the first class ends.

03:34 That is going to be where the next class begins.

03:41 And then we're going to add the class width to that, and we will get 105 ,834.

03:52 That's where the next class begins.

03:58 And we'll add that class with again.

04:02 We get 123 ,751.

04:07 We'll add the class width to that.

04:13 We'll add the and we'll add the class with one more time so that we have a total of six classes.

04:26 Now, if the second class is going to begin at 87 ,917, that means the first class has to end at 87 ,916.

04:40 And if the third class begins at 105 ,834, then the second class has to end at 8 ,916, and if the third class begins at 105 ,834, 105 ,833.

04:53 So you're just backing up one from where the next class starts.

04:58 So the third class will end at 123 ,750.

05:05 The next class will end at 141 ,66767...

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