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Pre-Algebra: Intro to Statistics

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Information about Pre-Algebra: Intro to Statistics
Education

Published on February 23, 2014

Author: ms_moran

Source: slideshare.net

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Mean, Median, Mode, Range and Stem and Whisker Plots
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Mean, Median, Mode and Range Introduction to Statistics Grade 7 Pre-Algebra Ms. Moran

Vocabulary • Mean  The sum of the data in a set divided by the number of items of data. Aka the average. • Median  The middle number of a group of data that has been arranged in numerical order. • Mode  The number that occurs most often. • Range  The difference between the greatest and the least numbers. 2

Mean • Does NOT refer to Ms. Van Beek! • How to find the mean of a group of data:  Take all the numbers and add them together.  Count how many numbers you added.  Divide the sum of the numbers by that number. • Example 1:  The weights of 9 students, measured in pounds, are recorded below. Find the mean weight. • 135, 120, 116, 119, 121, 125, 135, 131, 123 • Example 2:  The mean price of 5 items is $7.00. The prices of the first four items are $6.50, $8.00, $5.50 and $6.00. How much does the fifth item cost? 3

Median • How to find the median of a group of data:  Place all of the numbers in order in increasing value.  The middle number is the median.  If there are two middle numbers, then the median is the average of the two middle numbers. • Example 1:  The weights of 9 students, measured in pounds, are recorded below. Find the median of the weights. • 135, 120, 116, 119, 121, 125, 135, 131, 123 • Example 2:  The grade point averages of 10 students are listed below. Find the median grade point average. • 3.15, 3.62, 2.54, 2.81, 3.97, 1.85, 1.93, 2.63, 2.50, 2.80 4

Mode • How to find the mode of a group of data:  Tally the number of times each of the numbers appears in the group of numbers.  The mode is the number that is written the most often. • Example 1:  In a crash test, 11 cars were tested to determine what impact speed was required to obtain minimal bumper damage. Find the mode of the speeds given in miles per hour below. • 24, 15, 18, 20, 18, 22, 24, 26, 18, 26, 24 • Example 2:  A marathon race was completed by 5 participants. What is the mode of these times given in hours? • 2.7 hr, 8.3 hr, 3.5 hr, 5.1 hr, 4.9 hr 5

Range • How to find the range of a group of data:  Find the largest number of the group.  Find the smallest number of the group.  The range is the largest number minus the lowest number in a set of data. • Example 1:  The weights of 9 students, measured in pounds, are recorded below. Find the range of the weights. • 135, 120, 116, 119, 121, 125, 135, 131, 123 • Example 2:  The range of a set of numbers is 1,362. The largest number is 2,172. What is the smallest number? 6

Stem-and-Leaf Plots Box-and-Whisker Plots You can do it!

Stem-and-Leaf Plots • Data can be displayed in many ways. One method of displaying a set of data is with a stem-and-leaf plot.   A stem-and-leaf plot is a display that organizes data to  show its shape and distribution. • In a stem-and-leaf plot each data value is split into a  "stem" and a "leaf".  The "leaf" is usually the last digit of  the number and the other digits to the left of the "leaf"  form the "stem".   • The number 123 would be split as:   Stem 12  Leaf 3 8

Constructing a Stem-and-Leaf Plot • The data: Math test scores out of 50 points:    35, 36, 38, 40, 42, 42, 44, 45, 45, 47, 48, 49, 50, 50, 50. Writing the data in numerical  order may help to organize the  data, but is NOT a required step.   Ordering can be done later. 35, 36, 38, 40, 42, 42, 44, 45,  45, 47, 48, 49, 50, 50, 50 The number 38 would be represented as: Separate each number into a  stem and a leaf.  Since these are  Stem Leaf two digit numbers, the tens digit  is the stem and the units digit is  3 8 the leaf. Title the plot graph.  Group the  numbers with the same stems.   List the stems in numerical  order.  (If your leaf values are  not in increasing order, order  them now.) Prepare an appropriate legend  (key) for the graph. Math Test Scores (out of 50 pts) Stem Leaf 3 5 6 8 4 0 2 2 4 5 5 7 8 9 5 0 0 0 Legend: 3 | 6 means 36 9

Box-and-Whisker Plots • Data can be displayed in many ways. One method of displaying a set of data is with a box-and-whisker plot.   Box-and-whisker plots are helpful in interpreting the distribution  of data.  We know that the median of a set of data separates the data into two equal parts. Data can be further separated into quartiles. • The first quartile is the median of the lower part of the data. • The second quartile is another name for the median of the  entire set of data. • The third quartile is the median of the upper part of the data. • Quartiles separate the original set of data into four equal parts.   Each of these parts contains one-fourth of the data. 10

Constructing a Box-and-Whisker Plot • The data: Math test scores 80, 75, 90, 95, 65, 65, 80, 85, 70, 100 Write the data in numerical  order and find the first quartile,  the median, the third quartile,  the smallest value and the  largest value. median = 80 first quartile = 70 third quartile = 90 smallest value = 65 largest value = 100 Place a circle beneath each of  these values on a number line. Draw a box with ends through  the points for the first and third  quartiles.  Then draw a vertical  line through the box at the  median point.  Now, draw the  whiskers (or lines) from each  end of the box to the smallest  and largest values. 11

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