Range, Mean, Median, Mode Essential Question: How do we take a random sample, and what statistics can we find with the data? Standard: MM1D3.a.

Range, Mean, Median, Mode The first step to find range, mean, median, and mode is to organize your data by listing it from the smallest to largest number.

Tells how spread out the data is. Range Tells how spread out the data is.

Range The range of the data set is the difference between the largest and the smallest number in the set. To find the range, you simply subtract the smallest number from the largest number in the set. ( 1, 1, 2, 2, 2, 3, 4, 5, 5, 5, 5) Range = 5 – 1 = 4

MEAN The mean is the mathematical center The mean takes all numbers into consideration (use all of data to calculate the mean) The mean is affected by “extreme” data

The mean of the data set is its average. To find the mean, you add up all the numbers and divide the answer by how many numbers you have. ( 1, 1, 2, 2, 2, 3, 4, 5, 5, 5, 5) Mean = 3.18

Mean and Extreme data Imagine that 4 houses in rural western NC are worth the following: $27,000; $38,000; $42,000; $44,000. Let’s find the mean cost of these houses.

Mean and Extreme Data One day Oprah Winfrey flies over and decides to build a house on top of the mountain because of its scenic beauty. She builds a mansion worth $32,000,000. Before she built, the mean cost of a house on the mountain was $37,750. After Oprah Winfrey builds her dream house, the mean has shot up to $6,430,200!

Median The median is the number which is in the exact middle of the data set. ***YOUR DATA MUST BE ORDERED*** ( 1, 1, 2, 2, 2, 3, 4, 5, 5, 5, 5) Median = 3 Note: When your set of numbers is even you take the 2 middle numbers, add them, and divide by 2.

Mode The mode is the number that appears the most often. ( 1, 1, 2, 2, 2, 3, 4, 5, 5, 5, 5) Mode = 5 If no numbers are repeated, there is no mode. If more two numbers appear the most often there are two modes.

Range, Mean, Median, Mode Example 1. Two dice were thrown 10 times and their scores were added together and recorded. Find the range, mean, median, and mode for this data. 7, 5, 2, 7, 6, 12, 10, 4, 8, 9

Range, Mean, Median, Mode Example 2. Nine people took a vocabulary test. Their scores (out of 10) are recorded below. Find the range, mean, median, and mode for the test. 2, 9, 3, 7, 4, 8, 6, 10, 4

Box plots are useful for comparing two or more sets of data. Box and Whisker Plots Box plots are useful for comparing two or more sets of data.

Find the Minimum Value (lowest extreme) Step 1: Organize data, find the median Step 2: Find the First Quartile Q1 Step 3: Find the Third Quartile Q3 Step 4: Find the Minimum Value (lowest extreme) Step 5: Find the Maximum Value (highest extreme)

Box and Whisker Plots Example: The data for Math Test Scores 80, 75, 90, 95, 65, 65, 80, 85, 70, 100 Step 1: Organize data, find median. Median of all data, (second quartile) | 65, 65, 70, 75, 80, 80, 85, 90, 95, 100

Box and Whisker Plots Median of lower part (first quartile – Q1) Example cont’d: The data for Math Test Scores 80, 75, 90, 95, 65, 65, 80, 85, 70, 100 Step 2: Find first Quartile Median | 65, 65, 70, 75, 80, 80, 85, 90, 95, 100 Median of lower part (first quartile – Q1)

Box and Whisker Plots Median of upper part, (third quartile – Q3) Example cont’d: The data for Math Test Scores 80, 75, 90, 95, 65, 65, 80, 85, 70, 100 Step 3: Find 3rd Quartile Median | 65, 65, 70, 75, 80, 80, 85, 90, 95, 100 | | Median of lower part (first quartile) Median of upper part, (third quartile – Q3)

Box and Whisker Plots Example cont’d: The data for Math Test Scores 65, 65, 70, 75, 80, 80, 85, 90, 95, 100 Step 4: Find minimum value (lowest extreme) Minimum Value = 65 Step 5: Find maximum value (highest extreme) Maximum Value = 100

It’s time to construct our box and whisker plots! 5 Statistical Summary Median = 80 First Quartile (Q1) = 70 Third Quartile (Q3) = 90 Minimum = 65 Maximum = 100 It’s time to construct our box and whisker plots!

Box and Whisker Plots Place a circle beneath each of these values in relation to their location on an equally spaced number line.

Box and Whisker Plots 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. Box and Whisker Plots Then draw a vertical line through the box at the median point.

Box and Whisker Plots Now, draw the whiskers (or lines) from each end of the box to these minimum and maximum values.

Box & Whisker Plot Practice From the following data create a box-and-whisker plot: You must find the Median, Q1, Q3, Max, & Min 5, 7, 10, 12, 11, 11, 8 ______________________________ 61, 80, 76, 70, 90, 93, 50 _________________________________

Interquartile Range (IQR) We find the interquartile by subtracting Q3 – Q1 In this example, that would be 90 – 70 = 20, therefore, IQR = 20

Now You Try!! Find the median, Q1 , Q3 , minumum value, maximum value, and interquartile range. Then, construct a box plot using the following data. 12, 6, 4, 9, 8, 4, 9, 8, 5, 9, 8, 10