Math203 Ch3 notes

# Math203 Ch3 notes - Chapter 3 Data Descriptions In...

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Chapter 3: Data Descriptions In statistics, we like to describe what the data is telling us. It is important to distinguish between a statistic and a parameter. A statistic is obtained from a sample. A parameter is obtained from a population. We use both of these concepts to describe what is going on, statistically. This chapter goes over several ways to describe the data. Be careful on notations. We will sometimes have different notations for the sample verses the population. N = population total n = sample total number of observations. We will tend to discuss samples. Assume we are discussing statistics and not parameters (statistics are for the sample), unless otherwise noted.

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Chapter 3: Data Descriptions Measures of Central Tendencies Describes the “average” or the center Measures of Variations (or Dispersion) Describes the spread Measures of Position Describes the location
Measures of Central Tendency Mean Sample Mean: Population Mean: Add up all the data values and divide by the total number of observations/values We can obtain the mean for grouped data. Use the midpoint of each class as the observation. If a class of 12-16 has a frequency of 5, we would use the midpoint of 14 five times. The book gives examples and a formula. n X x = n X x = n X = μ

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Measures of Central Tendency Median median= middle. It is the midpoint of the ordered data. . If the number of data points is even, you must take the average of the 2 middle numbers. Your text denotes median MD. For smaller data sets, you can find the mean by arranging the data, then finding the middle number. Count a data point on each end and make your way to the middle number(s). For larger data sets, this is not feasible. Once the data is ordered, we can assign it a location number (1, 2, …, n). Divide the number in the data set by 2. If you get a whole number take the average of the data point in that location and the next location. If you get a decimal, round UP and take the data point in that location.
Measures of Central Tendency Mode mode=most. It is the value that occurs the most in the data set. There may not be a mode. There can be more than one mode. Bimodal is when there are 2 modes. Multimodal is the generic term for more than 1 mode. For grouped data, we have a modal class . The class with the highest frequency

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Measures of Central Tendency Midrange An estimate of the middle. It is the average of the highest and lowest ordered data value. The text denotes it MR 2 value highest value lowest MR + =
Measures of Central Tendency Weighted Mean : Use weights in the calculation of the mean. Used when the data values do not count the same

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Math203 Ch3 notes - Chapter 3 Data Descriptions In...

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