Normal Distribution and Standard Deviation

Experimental Science Background: Mean- The average of a set of numbers or the calculated central value. It the sum of the numbers divided by the number of values used n=the number of values used n Xi is the sum of all the values. i=1 The mean is equal to the sum of the number divided by the number of values used. Experimental Science

Averaging or Determining What is Normal The median is the middle number (in a sorted list of numbers). To find the median, place the numbers you are given in value order and find the middle number. Example: find the median of {13, 23, 11, 16, 15, 10, 26}. Put them in order: {10, 11, 13, 15, 16, 23, 26} and 15 is the median value.

Averaging or Determining What is Normal The mode is the value it appears most often (in a sorted list of numbers). 13, 13, 13, 13, 14, 14, 16, 18, 21 13 is the mode from the list above. The median is 14, while the mean is 15.

Data is skewed to the ________ How Will this data affect the mean?

Data is Skewed to the _________

If a number of data points are plotted on a histogram and the majority of points lie close to the average and fewer data points are found further from the average, it forms a bell shaped curve. This is called the normal distribution. If it is a true normal distribution, then the mean, mode and median should all occur at the same place. Experimental Science

Mean, Median, Mode is on the same line 50% of values is less than the mean * 50% of values is greater than the mean

Statistics, Analysis, and AP Biology Many thing when measured and plotted from large a population tend to form curves that approximate the normal distribution. These are World War I soldiers arranged in rows according to height. While the curve formed by these soldiers is not perfectly symmetrical, there is a cluster around the mean with rapidly tapering tails. Many traits like height, weight, and I.Q. form a normal distributions. Statistics, Analysis, and AP Biology

Histogram – A GRAPHICAL DISPLAY OF DATA USING BARS OF DIFFERENT HEIGHTS *SIMILAR TO BAR CHART Histogram groups numbers into ranges You decide what ranges to use

Frequency Distribution Table and Histograms Quite often there are too many data points to make individual bars so the data is grouped together in increments that have a particular range. These increments are called bins.

Frequency Distribution Table and Histograms Frequency distribution table shows how often a measurement occurs in a collection of data. Histogram is a type of bar graph that illustrates a frequency distribution. The horizontal represents the continuous measurements. The vertical axis represents the frequency of the measurements.

Creating a Histogram . The data from the mung beans approximates a normal distribution 0.01 g.

Two Different Normal Distributions How are these two histograms alike? How are they different? On the AP exam, both multiple choice and free response style questions visit this connection using graphical, analytical, and application-based stems. Let’s take a look at some recent free response questions that illustrate this concept:

Histograms Using 300 Seeds

Two Different Normal Distributions These two histograms have the same mean of five but they differ in their variation or range of values. Range=(Max value)- (Min value) Determine the range for the seeds that you measured the mass. Which has more variation pinto beans or black-eyed peas?