Measures of Central Tendency

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# Measures of Central Tendency - PowerPoint PPT Presentation

Measures of Central Tendency. Mean, Median, Mode. 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

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Presentation Transcript

### Measures of Central Tendency

Mean, Median, Mode
• 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.
Skewness – data is skewed if it is not symmetric and extends more to one side than the other.
• The one on the left is positively skewed.
• The one on the right is negatively skewed.

Mean

•  - 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

is the mean of a set of sample values

is the mean of all values in a population

mean from a frequency table

Median
• The method for finding the median is slightly different depending if the total f is even or odd.
• If Total f is odd, then there is one middle value. To find it, calculate Total f/2 = --- and round up.
• If Total f is even, then there are two middle values and the median is the average of these. To find the two middle values, calculate total f /2. The two middle scores are the ones corresponding to that number and the next. Once you have the two scores, the median is the average of them.
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

mean = \$107,600; median = \$8,500; mode = not one mode.

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

The mean is influenced by extreme scores (either low or high). Sometimes so much that it does not serve well as a typical value.

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

Mean: 420/7 = 60 (average daily intake of fat for 2000 calorie/day should be 65!)

Median: 58

Mode: 70

Below you will see a histogram that displays the frequency distribution of a sample of singers’ height of voices.

Find the mean, median, mode.

Below you will see a histogram that displays the frequency distribution of a sample of singers’ height of voices.

Find the mean, median, mode.

Below you will see a histogram that displays the frequency distribution of a sample of singers’ height of voices.

Find the mean, median, mode.

Below you will see a histogram that displays the frequency distribution of a sample of singers’ height of voices.

Find the mean, median, mode.

Below you will see a histogram that displays the frequency distribution of a sample of singers’ height of voices.

Find the mean = 70.8, median =71, mode = 72.