# 1. Statistics 2. Frequency Table 3. Graphical Representations  Bar Chart, Pie Chart, and Histogram 4. Median and Quartiles 5. Box Plots 6. Interquartile.

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1. Statistics 2. Frequency Table 3. Graphical Representations  Bar Chart, Pie Chart, and Histogram 4. Median and Quartiles 5. Box Plots 6. Interquartile Range and Five-Number Summary 1

 Statistics is the branch of mathematics that deals with data: their collection, description, analysis, and use in prediction.  Data can be presented in raw form or organized and displayed in tables or charts. 2

 A table like the one below is called a frequency table since it presents the frequency with which each response occurs. 3

 This graph shows the same data as the previous example as a bar chart. 4

 The pie chart consists of a circle subdivided into sectors, where each sector corresponds to a category. The area of each sector is proportional to the percentage of items in that category. This is accomplished by making the central angle of each sector equal to 360 times the percentage associated with the segment. 5

 The pie chart of the data of the previous example is: 6

 When the data is numeric data, then it can be represented by a histogram which is similar to a bar chart but there is no space between the bars. 7

8 The grades for the first quiz in a class of 25 students are 8 7 6 10 5 10 7 1 8 0 10 5 9 3 8 6 10 4 9 10 7 0 9 5 8. ( a ) Organize the data into a frequency table. ( b ) Create a histogram for the data.

GradeNumber 105 93 84 73 62 53 41 31 20 11 02 9

 The median of a set of numerical data is the data point that divides the bottom 50% of the data from the top 50%. To find the median of a set of N numbers, first arrange the numbers in increasing or decreasing order. The median is the middle number if N is odd and the average of the two middle numbers if N is even.  The quartiles are the medians of the sets of data below and above the median. 11

GradeNumber 105 93 84 73 62 53 41 31 20 11 02 12 For the grade data given, ( a ) find the median; ( b ) find the quartiles.

GradeNumber 105 93 84 73 62 53 41 31 20 11 02 13 N = 25 so median is the 13 th grade: 7. There are 12 grades in the lower and upper halves. The upper quartile is the average of the 19 th and 20 th grade: Q 3 = (9 + 9)/2 = 9. The lower quartile is the average of the 6 th and 7 th grade: Q 1 = (5 + 5)/2 = 5.

 Graphing calculators can display a picture, called a box plot, that analyzes a set of data and shows not only the median, but also the quartiles, lowest data point (min) and largest data point (max). 14

15 GradeNumber 105 93 84 73 62 53 41 31 20 11 02 For the grade data given, find the box plot. 0 5 7 9 10

 The length of the rectangular part of the box plot, which is Q 3 - Q 1, is called the interquartile range.  The five pieces of information, min, max, Q 2 = median, Q 1 and Q 3 are called the five-number summary. 16

17 For the grade data from the previous example, list the five-number summary and the interquartile range. 0 5 7 9 10 min = 0, Q 1 = 5, Q 2 = median = 7, Q 3 = 9, max = 10 Interquartile range is Q 3 - Q 1 = 9 - 5 = 4.

 Bar charts, pie charts, histograms, and box plots help us turn raw data into visual forms that often allow us to see patterns in the data quickly.  The median of an ordered list of data is a number with the property that the same number of data items lie above it as below it. For an ordered list of N numbers, it is the middle number when N is odd, and the average of the two middle numbers when N is even. 18

 For an ordered list of data, the first quartile Q 1 is the median of the list of data items below the median, and the third quartile Q 3 is the median of the list of data items above the median. The difference of the third and first quartiles is called the interquartile range. The sequence of numbers consisting of the lowest number, Q 1, the median, Q 3, and the highest number is called the five-number summary. 19

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