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Understanding Central Tendency

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Questions and Answers

What is the primary purpose of a central tendency?

To calculate the mode of a dataset

To summarize data with a single number (correct)

To compare datasets with different units

To find the highest value in a dataset

What is the mode in the given dataset of flower heights?

19 (correct)

How is the mean calculated in the given dataset?

By finding the middle value in the dataset

By adding up all values and dividing by the number of values (correct)

By finding the highest value in the dataset

By finding the lowest value in the dataset

What is the median in the given dataset of flower heights?

19 Signup and view all the answers

Why is the median a better measure of central tendency in this dataset?

Because it is affected less by extreme values Signup and view all the answers

What is the purpose of the 'middle' trick for remembering the median?

To help distinguish between mode and median Signup and view all the answers

Why is the value 19 a good summary of the dataset?

Because it appears most frequently in the dataset Signup and view all the answers

What is the mode of a dataset?

The value that appears most often Signup and view all the answers

What is the mean of a dataset?

The sum of the dataset divided by the number of values Signup and view all the answers

What is the median of a dataset?

The middle value in the dataset when it's in numerical order Signup and view all the answers

Why do you need to put the dataset in numerical order?

To find the median of the dataset Signup and view all the answers

What is the median of the dataset {58, 60, 61, 64, 65, 65, 66, 66, 66, 68, 69, 71, 73, 74, 78}?

66 Signup and view all the answers

How do you calculate the mean of a dataset?

Add up all the values and divide by the number of values Signup and view all the answers

What is the mode of the dataset {58, 60, 61, 64, 65, 65, 66, 66, 66, 68, 69, 71, 73, 74, 78}?

66 Signup and view all the answers

Why do you need to be careful when you're given a dataset?

Because the dataset might not be in numerical order Signup and view all the answers

Study Notes

Measures of Central Tendency

Central tendency is a way of summarizing data with a single number.
The three basic measures of central tendency are mode, mean, and median.

Mode

The mode is the number found most often in a dataset.
Example: in the dataset 10, 15, 18, 19, 19, 19, 22, 24, 35, 40, 45, the mode is 19.

Mean

The mean is the average of a dataset.
To calculate the mean, add up all the values and divide by the number of values.
Example: in the dataset 10, 15, 18, 19, 19, 19, 22, 24, 35, 40, 45, the mean is 24.2.

Median

The median is the number in the middle of a sorted dataset.
To find the median, count the number of values and find the middle value.
If there are two middle values, the median is the number halfway between them.
Example: in the dataset 10, 15, 18, 19, 19, 19, 22, 24, 35, 40, 45, the median is 19.

Example Problem

Measure the heights of 15 people in a grocery store: 58, 60, 61, 64, 65, 65, 66, 66, 66, 68, 69, 71, 73, 74, 78.
The mode is 66, the mean is 66.9, and the median is 66.