In 3-8, find the mean, the median, and the mode for each set...

In $3-8,$ find the mean, the median, and the mode for each set of data.
$$
\begin{array}{|r|r|}\hline x_{i} & {f_{i}} \\ \hline 10 & {1} \\ {9} & {1} \\ {8} & {3} \\ {7} & {7} \\ {6} & {6} \\ {5} & {2} \\ {4} & {2} \\ \hline\end{array}
$$

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Key Concepts

Measures of Central Tendency

Measures of central tendency are statistical tools used to summarize and describe the center or typical value of a data set. They include the mean, median, and mode, each providing a different perspective on what constitutes a 'central' value in the data.

Mean

The mean is the arithmetic average of a set of data values. When dealing with frequency distributions, it is calculated by multiplying each data value by its corresponding frequency, summing these products, and then dividing the result by the total number of observations. This provides a single value that represents the overall level of the data.

Median

The median is the middle value in a data set when the data is arranged in ascending (or descending) order. In a frequency distribution, it is determined by finding the data point that divides the distribution such that 50% of the observations lie below it and 50% lie above it. The median is particularly useful as a measure of central tendency in skewed distributions.

Mode

The mode is the data value that occurs most frequently within a data set. In a frequency distribution table, it is the value associated with the highest frequency. The mode is useful for identifying the most common or popular value, especially in categorical data.

Transcript

00:01 All right, so for number six, we are going to look at the given table and we need to extend on that table.

00:08 So first things first, before we work with the extension to find the mean, median mode, we need to go ahead and add up our frequencies.

00:17 So in this table, we have 1 .137, 6, 2, and 2.

00:22 When you add up all of those numbers together, you're going to get 22.

00:29 And then in order to find the mean, you're going to have to multiply each number in the list times its frequency.

00:35 So in this case, 10 times 1, for example.

00:38 So that's going to be a 10.

00:41 9 times 1 is 9.

00:43 8 times 3 is going to be 24.

00:47 7 times 7 is 49.

00:51 6 times 6 is 36.

00:55 5 times 2 is 10.

00:59 4 times 2 is 8.

01:00 And so we need to add up all the numbers that we just multiplied to get our big number for our mean that we're going to use.

01:08 So we're going to add up 10 plus 9 plus 24 plus 49 plus 36 plus 10 plus 8 and we're going to get 146.

01:24 So we're going to take the big number divided by the little number here at the mean.

01:27 So we're going to do 146 divided by 22.

01:35 And that's going to be approximately 6 .6.

01:41 All right.

01:43 So in order to get the median, you're going to need to go get the cumulative frequency.

01:48 That's why there's that extra column now...

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