Mean,Median, Mode Teacher Twins 2015
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1 Mean,Median, Mode Teacher Twins 2015
2 Warm Up How can you change the non-statistical question below to make it a statistical question? How many pets do you have? Possible answer: What is your favorite type of pet or animal?
3 Mean, Median, Mode and Range Mean (Average)- the sum of the data divided by the number of items in the set of data. Median- The middle number in a set of data that is written in order. Mode- The data item that occurs most often. Range- The highest value the lowest value.
4 Median Mode There is no mode because each test grade is different. Range
5 Median Mode The mode is Range
6 Outlier- An extreme value in a set of data. 23, 34, 27, 33, 121 When each measure is most useful Mean- The data are spread fairly evenly. Median-The data set has an outlier. Mode- The data involve a subject in which many data points of one value are important, such as results of an election
7 Mean-5.9 Median-5 The median best represents the data because 24 is an outlier and causes the mean to be higher.
8 Practice 1). Find the mean, median, mode and range. Number of students absent during school this week. 2). Find the mean, median and mode. Which one best represents his grades? Explain. Jayden s test scores 50, 86, 95, 80, 90, 88, 87, 95 Mean-83.9 Median-87.5 Mode -95
9 Closure Why do you need to find the mean, median or mode of a set of data?
10 Dot Plots and Measures of Center Teacher Twins 2015
11 Warm Up Find the mean, median, mode and range for each set of data. 1). 45, 67, 34, 43, 56, 67 2). 121, 234, 300, 121, 234 3). 34, 67, 87, 23, 12, 98, 56
12 A dot plot shows the frequency of data on a number line. It is best to use a dot plot when you do not have a lot of data.
13 The distribution of a dot plot shows the arrangement of the values of a data set. A symmetrical graph shows the same number of points below and above the middle point. How many books did you read over the summer? This graph is symmetrical.
14 A dot plot is skewed right if most of the data are clustered to the left or the lower data values. How many books did you read over the summer?
15 A dot plot is skewed left if most of the data are clustered to the right or the higher values. How many books did you read over the summer?
16 Measures of Center Data sets have many numerical values. You can summarize the data with one number called a measure of center. Mean and median are measures of center. The median is a more useful measure of center if the data is skewed.
17 Example 1: Which measure of center would best represent this data? How many books did you read over the summer? Mean-7.9 Median-8.5 The median best represents the data because it is skewed.
18 Example 2: Which measure of center would best represent this data? Science Test Grades Mean-70 Median-70 The median and mode best represents the data because it is not skewed.
19 Practice Find each measure of center and tell which best represents the data. 1). How many brothers and sisters do you have? 2).How many pets do you have?
20 Closure Why do we need to use measures of center such as the mean and median to represent data? It summarizes the data in one number.
21 Mean Absolute Deviation Teacher Twins 2015
22 Warm Up Practice Tell which measure of central tendency best represents the data. 1). How many pairs of shoes do you have? How is the The data is skewed left. data skewed? The best measure is the median because it is slightly skewed. 2). How many hours do you play video games daily? How is the data skewed? The data is somewhat symmetrical. Both the mean and median represent the data.
23 Mean Absolute Deviation Mean Absolute Deviation is the average distance between each piece of data and the mean. The MAD is a measure of variation. Measures of variation describe how data values vary by using a single number.
24 How to Find the Mean Absolute Deviation or MAD 1). Find the mean. 2). Find the distance between each piece of data and the mean. Remember distance is not negative so take the absolute value of the difference. 3). Find the average of the differences.
25 Example 1: Find the mean absolute deviation of the daily visitors to the local park for one week. 234, 540, 502, 629, 530, 450, 574 Find the average Find the distance each piece of data is from the average. Find the average of the differences.
26 Example 1: Find the mean absolute deviation of the daily visitors to the local park for one week. 234, 540, 502, 629, 530, 450, 574
27 Example 2: Find the mean absolute deviation of the price of movie tickets. $5.75, $5.00, $6.50, $7.00, $9.00, $9.50 Find the average. $7.13 Find the distance each piece of data is from the average. Find the average of the differences.
28 Example 2: Find the mean absolute deviation of the price of movie tickets. $5.75, $5.00, $6.50, $7.00, $9.00, $9.50
29 Practice Find the mean absolute deviation. Round to the nearest tenth. Explain what the MAD tells you about the spread of the data. 1). Number of Pets per household 4, 5, 8, 0, 3, 2 2). Hours spent per week on homework 15, 6, 2, 8, 9, 7
30 Closure What does the mean absolute deviation tell you about your data?
31 Histograms TeacherTwins 2015
32 Warm Up Practice Find the mean absolute deviation. Round to the nearest tenth. Explain what the MAD tells you about the spread of the data. 1). Number of rooms in your house 4, 5, 8, 10, 6, 7 2). Hours spent per week exercising 10, 6, 2, 8, 9, 7
33 Histograms A histogram is similar to a bar graph. Histograms show the frequency of data in intervals of the same size.
34 Example 1: Create a histogram of the following data. Ages of people riding the Ro Roller Coaster.
35 Example 1: Create a histogram of the following data. When you look at the spread of the data you can see that it is skewed to the right. The mean is probably larger than the median. Ages of people riding the Ro Roller Coaster.
36 Example 1: Find the median age of the people riding the Ro Roller Coaster. 57 people were surveyed. The median age is Ages of people riding the Ro Roller Coaster.
37 Example 2: Create a histogram of the following data. Books Read Over the Summer.
38 Example 2: Create a histogram of the following data. Books Read Over the Summer.
39 Example 2: Find the median amount of books read during the summer. Books Read Over the Summer.
40 Practice 1).Create a histogram of the data. 2).Describe the spread of the data. 3). Find the median of the data.
41 Practice
42 Closure How is a histogram like a dot plot? How are they different?
43 Measures of Variation TeacherTwins 2015
44 Warm Up 1).Create a histogram of the data. 2).Describe the spread of the data. 3). Find the median of the data.
45 Warm Up 1). 2).Describe the spread of the data. The data is symmetrical 3). Find the median of the data. The median is
46 Flippable
47 Measures of Variation are used to describe the distribution of data. We have already learned about one measure of variation called the range. The range is the difference between the largest data value and the smallest.
48 To find the range you need to use the extremes. Lower Extreme Upper Extreme Lower Extreme or Minimum- Lowest number in set of data. Upper Extreme or Maximum- Highest number in set of data.
49 Quartiles are the values that divide the data into quarters. UQ LQ Lower quartile (LQ) The median of the lower half of a set of data also called Q1. Upper Quartile (UQ) The median of the upper half of a set of data also called Q3.
50 Quartiles Quartiles are the values that divide the data into quarters.
51 Example 1: MedianLower QuartileUpper QuartileInterquartile RangeUpper ExtremeLower Extreme-
52 Example 2: MedianLower QuartileUpper QuartileInterquartile RangeUpper ExtremeLower Extreme-
53 Practice Prices of Movie Theatre Tickets $5.00 $7.50 $7.50 $5.75 $6.00 $9.50 $9.00 $10.00 $9.00 MedianLower QuartileUpper QuartileInterquartile RangeUpper ExtremeLower Extreme-
54 Closure Explain how you find the interquartile range of the following set of data. 176, 156, 143,155, 167, 180
55 Box-and-Whisker Plots TeacherTwins 2015
56 Warm Up Find the interquartile range and range for each set of data. 1). Joe s Grades 55, 67, 94, 83,87,74, 70 2). Weights of the wrestling team 121, 134, 175, 123, 152 3). Weekly earnings during the summer $34, $67, $87, $23, $12, $98, $56
57 Box and whisker plots divide your data into 4 parts or quartiles. The middle of the data is the median. 50% of the data is in the box.
58 How to Make Box-and-Whisker Plots 1). Find the smallest and largest number. Draw and label a number line that covers the range of the data. 2). Find the median, the extremes, and the upper and lower quartiles. Mark these points above the number line. 3). Draw a box around your quartiles. Draw a vertical line in the box for the median. 4). Draw lines from the box to each extreme.these are the whiskers.
59 Example 1: Create a box-and-whisker plot of the following data. Daily visitors to the local park for one week. 234, 540, 502, 629, 530, 450, 574 Lower Quartile Upper Quartile Median Lower Extreme Upper Extreme
60 Example 1: Create a box-and-whisker plot of the following data. Daily visitors to the local park for one week. 234, 540, 502, 629, 530, 450, 574 Lower Quartile Upper Quartile Median Lower Extreme Upper Extreme
61 Example 1: Daily visitors to the local park for one week. 234, 540, 502, 629, 530, 450, 574 Is the data skewed left, skewed right, or symmetrical?
62 Example 2: Create a box-and-whisker plot of the following data. Price of movie tickets $5.75, $5.00, $6.50, $7.00, $9.00, $9.50 Lower Quartile Upper Quartile Median Lower Extreme Upper Extreme
63 Example 2: Create a box-and-whisker plot of the following data. Price of movie tickets $5.75, $5.00, $6.50, $7.00, $9.00, $9.50 Lower Quartile Upper Quartile Median Lower Extreme Upper Extreme
64 Example 2: Price of movie tickets $5.75, $5.00, $6.50, $7.00, $9.00,$9.50 1).Is the data skewed left, skewed right, or symmetrical? 2). What percent of the movie ticket prices are between $5.75 and $9.00? 3). What is the interquartile range?
65 Practice 1). Make a box-and-whisker plot of the following test scores. 50, 55, 60, 70, 75, 75, 100 Lower Quartile Upper Quartile Median Lower Extreme Upper Extreme
66 Practice 2). Use the box-and-whisker plot from question 1 to answer the following questions. a). Describe the spread of the data. b). What percent of the grades were higher than 75? c). What is the IQR?
67 Closure How does a box-and-whisker plot divide data?
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