Chapter 5: Measures of Central Tendency



Chapter 5: Measures of Central Tendency - values that the data tends to center around

mean – also known as the arithmetic mean or average. Calculated by adding the scores and dividing by the number of scores

median – the number in the middle when the data is arranged in ascending or descending order

mode – the most frequent. If two numbers occur the same amount of times the set is bimodal. If all the same, more than one mode.

midrange – skip

Notation:

( - denotes summation of a set of values

x – is the variable usually used to represent the individual data values

n – represents the number of values in a sample

N – represents the number of values in a population

[pic]is the mean of a set of sample values

[pic] is the mean of all values in a population

[pic] mean from a frequency table

Skewness - A frequency distribution is either symmetric or skewed. For a symmetric distribution the mean, the mode and the median are all the same. When the distribution is cut into two halves (right at the center) one side is a perfect replicate of the other. Normal Distribution (ND) is an example of this

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|[pic] |[pic] |[pic] |

|Symmetric. | | |

| |Skewed to right (positively skewed). | |

| | |Skewed to left (negatively skewed). |

Examples:

1. Compute the mean, median, and mode for the following 10 incomes:

$10,000 $8,000 $7,000 $5,000 $7,000 $1,000,000 $9,000 $11,000 $8,000 $11,000

Which measure of central tendency is most meaningful in this case and why?

2. Below is the fat content of some of our favorite meals. Compute the mean, median, and mode.

|Sandwich |Grams of fat |

|Whopper and King size fries |70 |

|Wendy’s Big Bacon Classic with Biggie Fries |53 |

|Quarter Pounder with Cheese and large fries |56 |

|Big Mac with large fries |58 |

|Arby’s Regular Roast Beef and large curly fries |50 |

|Arby’s Big Montana and large curly fries |70 |

|Angus Big Bacon & Cheese Steak and King size fries |63 |

Mean: Median: Mode:

3. Below you will see a histogram that displays the frequency distribution of a sample of singers’ height of voices. Examine the graph and answer the questions that follow.

[pic]

Complete the table below according to the graph.

|Height |Frequency |xf |

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Find the mean, the mode and the median for this distribution.

Example 3: Below you will see a histogram that illustrates the frequency distribution of the scores obtained from a test. Examine the graph and answer the questions listed below it.

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|[pic] |Score |

| |Frequency |

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| |a. Construct a table that displays the |

| |frequency distribution |

b. Find the mean, median and the mode.

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