Data Analysis Data Analysis Statistics a powerful tool

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Data Analysis

Data Analysis

Data Analysis Statistics - a powerful tool for analyzing data 1. Descriptive Statistics -

Data Analysis Statistics - a powerful tool for analyzing data 1. Descriptive Statistics - provide an overview of the attributes of a data set. These include measurements of central tendency (frequency histograms, mean, median, & mode) and dispersion (range, variance & standard deviation) 2. Inferential Statistics - provide measures of how well your data support your hypothesis and if your data are generalizable beyond what was tested (significance tests)

Measurements of Central Tendency Data Set: 2 red, 3 blue, 1 green, 2 yellow,

Measurements of Central Tendency Data Set: 2 red, 3 blue, 1 green, 2 yellow, 2 black Frequency Histogram - 3 2 1 red blue green yellow black Mean - sum of data divided by the number of data points Median - middlemost data point when data are arrayed in sequence (lowest to highest) Mode - most frequently occurring value

Class Example Create a frequency distribution from the data in column A of the

Class Example Create a frequency distribution from the data in column A of the spreadsheet “Data Set D”. Use a class interval of 1.

Histogram of X 1: Data Set D 16 14 12 Count 10 8 6

Histogram of X 1: Data Set D 16 14 12 Count 10 8 6 4 2 0 0 1 2 3 4 5 6 7 8 9 10 11

Class Example Calculate the mean of the 500 numbers found in column A of

Class Example Calculate the mean of the 500 numbers found in column A of “Data Set C”. You may use any function except the “AVERAGE” function.

Determine the median of the following set of numbers: 4. 0, 2. 4, 6.

Determine the median of the following set of numbers: 4. 0, 2. 4, 6. 7, 3. 2, 6. 9, 5. 6, 3. 9, 5. 5 Class Example Determine the median of the 500 numbers found in column A of “Data Set C”.

Determine the mode of the following set of numbers: 3, 5, 2, 6, 5,

Determine the mode of the following set of numbers: 3, 5, 2, 6, 5, 1, 7, 3, 8, 5, 8, 2, 9, 0, 3, Class Example Determine the mode of the 500 numbers found in column A of “Data Set C”.

Measurements of Dispersion Data Set: Student A B C D E F G Exam

Measurements of Dispersion Data Set: Student A B C D E F G Exam I 90 95 85 90 95 Exam II 100 80 70 85 95 100 Range: highest and lowest values Variance: s 2= x – 2 x) 2 n n– 1 Standard Deviation: the square root of variance Standard Error of the mean: sx = s √n

Calculate the standard deviation of the following data set. 3, 7, 2, 8, 4,

Calculate the standard deviation of the following data set. 3, 7, 2, 8, 4, 6, 2, 8, 1, 0, 4, 6, 2, 8, 9

Which of the following two sets of data show the greatest amount of dispersion

Which of the following two sets of data show the greatest amount of dispersion around their mean? A: 2, 6, 1, 7, 3, 8, 4, 9, 10, 4, 5 B: 14, 65, 28, 70, 46, 52, 78, 38, 47, 34, 55

Class Example Calculate the mean, median, mode, range, standard deviation, standard error and variance

Class Example Calculate the mean, median, mode, range, standard deviation, standard error and variance of the data shown in column A of “Data Set D”.