Mean, Median, and Mode

Mean, Median, and Mode An Introduction to Data Management: Measures of Central Tendencies

Why Analyze Data? Data is collected to answer questions. When we want to answer a question, we collect data to provide information on that topic. We take the collected data and analyze it to find out if there are any relationships. DATA IS COLLECTED TO FIND ANSWERS TO MANY DIFFERENT QUESTIONS.

The Mean The sum of a list of numbers, divided by the total number of numbers in that list (average is another word for mean)

What Does SUM Mean? The answer to an addition problem. For example, the sum of 1 and 2 is 3. 1+2=3

How To Find The Mean Question A farmer wanted to know the daily mean for the number of eggs laid by his prize hen for the last seven days. The hen laid 4 eggs on Sunday, 3 eggs on Monday, 1 egg on Tuesday, 4 eggs on Wednesday, 2 eggs on Thursday, 0 eggs on Friday, and 4 eggs on Saturday. • Find the sum of the numbers • 4+3+1+4+2+0+4 = 18 • Divide the sum by how many numbers you have • 18÷7 = 2.6 • Mean = 2.6 • The hen laid an average of 2.6 eggs per day during that 7 day period.

Your Turn… To find the mean first you_________________, then _________________________

Checking Your Answer • Find the sum of the numbers • 12+16+25+10+32=95 • Divide the sum by how many numbers you have • 95÷5=19 • The daily average of milk cartons sold from the vending machine during the first week of school was 19 milk cartons per day.

Find The MeanSHOW YOUR WORK –GET IN THE HABIT NOW! • {8, 9, 12, 16, 18} • {1, 2, 4, 4, 5, 7, 11} • {25, 26, 27, 36, 42, 52} • {120, 134, 165, 210, 315}

Find The Mean • {8, 9, 12, 16, 18} 8+9+12+16+18 = 63÷5 = 12.6 • {1, 2, 4, 4, 5, 7, 11} 1+2+4+4+5+7+11 = 34÷5 = 4.9 3. {25, 26, 27, 36, 42, 52} 25+26+27+36+42+52 = 209÷6 = 34.8 4. {120, 134, 165, 210, 315, 356} 120+134+165+210+315+356 = 1300÷5 = 216.7

The Median The middle value in a list of numbers

How To Find The Median Question The eggs laid by a prize hen were recorded for a week. The hen laid 4 eggs on Sunday, 3 eggs on Monday, 1 egg on Tuesday, 4 eggs on Wednesday, 2 eggs on Thursday, 0 eggs on Friday, and 4 eggs on Saturday. What is the median? • Place the numbers in order, from least to greatest. • 0, 1, 2, 3, 4, 4,4 • Find the number that is in the middle of the data set • 0, 1, 2, 3, 4, 4, 4 • 3 is the median of this data set.

Your Turn… Question The number of milk cartons sold from the school vending machine were recorded for the first full week of school. 12 were sold on Monday, 16 were sold on Tuesday, 25 were sold on Wednesday, 10 were sold on Thursday, and 32 were sold on Friday. What is the median?

Checking Your Answer • Place the numbers in order, from least to greatest. • 10, 12, 16, 25, 32 • Find the middle value • 10, 12, 16, 25, 32 • The median for this data set is 16.

Oh Oh!!! What do you do if there are an even amount of numbers in your data set? < 2 middle numbers > {10, 12, 16, 18, 20, 24} You take the average of the two middle values. 16+18 = 34÷2 = 17 The median of this data set is 17.

Find The Median • {8, 9, 12, 16, 18} • {4, 2, 6, 4, 1, 7, 11} • {25, 26, 27, 36, 42, 52} • {120, 134, 165, 210, 315, 356}

Find The Median • {8, 9, 12, 16, 18} 8, 9, 12, 16, 18 • {4, 2, 6, 4, 1, 7, 11} 1,2, 4,4, 6, 7, 11 3. {25, 26, 27, 36, 42, 52} 25, 26,27,36, 42, 52 = 27+36 =31.5 • {120, 134, 165, 210, 315, 356} 120, 134,165,210, 315, 356 =187.5

The Mode The most common value or the value with the highest frequency in a data set.

How To Find The Mode Question The eggs laid by a prize hen were recorded for a week. The hen laid 4 eggs on Sunday, 3 eggs on Monday, 1 egg on Tuesday, 4 eggs on Wednesday, 2 eggs on Thursday, 0 eggs on Friday, and 4 eggs on Saturday. What is the mode? • Place the numbers in order, from least to greatest. • 0, 1, 2, 3, 4, 4,4 • Find the number that has the highest frequency in the data set. • 0, 1, 2, 3, 4, 4, 4 • 4 is the mode of this data set.

Your Turn… Question The number of milk cartons sold from the school vending machine were recorded for the first full week of school. 12 were sold on Monday, 16 were sold on Tuesday, 25 were sold on Wednesday, 10 were sold on Thursday, and 32 were sold on Friday. What is the mode?

Checking Your Answer • Place the numbers in order, from least to greatest. • 10, 12, 16, 25, 32 • Find the value that has the highest frequency in the data set. • 10, 12, 16, 25, 32 • There is no mode for this data set.

Find The Mode • {8, 9, 12, 16, 18} • {1, 2, 4, 4, 5, 7, 11} • {25, 26, 27, 36, 42, 52} • {120, 134, 165, 210, 315, 356}

Find The Mode • {8, 9, 12, 16, 18} There is no mode in this data set. • {1, 2, 4, 4, 5, 7, 11} The mode is 4. 3. {25, 26, 27, 36, 42, 52} There is no mode in this data set. 4. {120, 134, 165, 210, 315, 356} There is no mode in this data set.

Oh Oh!!! What do you do if there is more than one value that occurs at the highest frequency? {10, 12, 12, 16, 18, 18, 20, 24} The mode for this data set is 12 and 18. You can have more than one mode for a data set.

Finding The Range • Range: The distance between the maximum and the minimum number Range = Max – Min Example: 4, 6, 30, 24 Range = 30 – 4 Range = 26

Find The Range • {8, 9, 12, 16, 18} 18 – 8 = 10 The range is 10 • {3, 5, 2, 4, 5, 7, 2} 7 – 2 = 5 The range is 5. Finding the range is easier if you put the numbers in order from least to greatest first {120, 134, 165, 210, 315, 356} 356 – 120 = 234 The range is 234

Any Questions ???

Mean, Median, and Mode