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SECTION 6.6 Stem-and-Leaf Plots and Mean, Median, and Mode WHAT’S IMPORTANT: -- Be able to make and use a stemand-leaf plot to put data in order. -- Be able to find the mean, median, and mode of data. Section 6.6: “Stem-and-Leaf Plots and Mean, Median, and Mode” Stem-and-Leaf Plot: An arrangement of digits that is used to display and order numerical data. The stems are usually all digits except the last digit. The leaves are usually the last digit. For example, the number in the plot below is 45. Stem 4 Leaf 5 Section 6.6: “Stem-and-Leaf Plots and Mean, Median, and Mode” Example: The data shows the ages of 24 patients who were treated in one day at a health clinic. Make a stem-and-leaf plot of the data. 25 12 30 20 15 21 16 13 18 27 43 23 19 22 20 67 53 19 25 66 35 11 20 37 Stem Leaf 1 1 2 3 5 6 8 9 9 2 0 0 0 1 2 3 5 5 7 3 0 5 7 4 3 5 3 Key: 4|3 = 43 6 6 7 Section 6.6: “Stem-and-Leaf Plots and Mean, Median, and Mode” Example: The data shows the ages of 10 runners on the track team. Make a stem-andleaf plot of the data. 15 25 12 36 48 10 12 30 12 17 Stem 1 2 3 4 Leaf 0 2 2 2 5 7 5 0 6 8 Key: 4|8 = 48 Section 6.6: “Stem-and-Leaf Plots and Mean, Median, and Mode” Mean: Another word for “average”. Found by adding the numbers up and dividing the sum by the amount of numbers present. Median: The middle number when the numbers are written in order. If there is no “middle number”, then you add the two middle numbers and divide by 2. Mode: The number that occurs most frequently. A set of data can have more than one mode….or no mode. Section 6.6: “Stem-and-Leaf Plots and Mean, Median, and Mode” Example: Find the mean, median, and mode of the data given. 4, 2, 10, 6, 10, 7, 10 Mean = 49/7 = 7 2, 4, 6, 7, 10, 10, 10 Median = 7 Mode = 10 Section 6.6: “Stem-and-Leaf Plots and Mean, Median, and Mode” Example: Find the mean, median, and mode of the data given. 8, 5, 6, 6, 5, 6 Mean = 36/6 = 6 5, 5, 6, 6, 6, 8 Median = 6 Mode = 6 Section 6.6: “Stem-and-Leaf Plots and Mean, Median, and Mode” Make a stem-and-leaf plot of the data. 11 30 24 41 22 18 14 32 11 62 Stem 1 2 3 4 5 6 Leaf 1 1 4 8 2 4 0 2 1 Key: 4|1 = 41 2 Section 6.6: “Stem-and-Leaf Plots and Mean, Median, and Mode” Example: Find the mean, median, and mode of the data given. Mean = 440/10 = 44 Median = (44 + 50)/2 = 94/2 = 47 Mode = 51 Leaf Stem 3 0 3 4 4 2 4 5 0 1 1 1 4 Key: 3|0 = 30 Section 6.6: “Stem-and-Leaf Plots and Mean, Median, and Mode” Example: Find the mean, median, and mode of the data given. 5, 3, 10, 13, 8, 18, 5, 17, 2, 7, 9, 10, 4, 1 Mean = 112/14 = 8 1, 2, 3, 4, 5, 5, 7, 8, 9, 10, 10, 13, 17, 18 Median = 7.5 Mode = 5 and 10 Section 6.6: “Stem-and-Leaf Plots and Mean, Median, and Mode” Example: Find the mean, median, and mode of the data given. Mean = 657/24 = 27.375 Median = (21 + 22)/2 = 43/2 = 21.5 Mode = 20 Stem 1 2 3 4 5 6 Leaf 1 2 3 5 6 8 9 9 0 0 0 1 2 3 5 5 7 0 5 7 3 3 Key: 5|3 = 53 6 7 ► 1. Solve |𝟐𝒙 − 𝟓| = 𝟏𝟏 𝟐𝒙 − 𝟓= 11 or 𝟐𝒙 − 𝟓= −𝟏𝟏 +5 +5 +5 + 5 𝟐𝒙 = 16 𝟐𝒙 = −𝟔 𝟐 𝟐 𝟐 𝟐 𝒙= 𝟖 or 𝒙 = −𝟑 𝒙 = −𝟑, 𝟖 ► 2. Solve |𝟒𝒙 − 𝟐| = 𝟐𝟐 𝟒𝒙 − 𝟐 = 𝟐𝟐 or +𝟐 + 𝟐 𝟒𝒙 = 𝟐𝟒 𝟒 𝟒 𝒙=𝟔 or 𝟒𝒙 − 𝟐 = −𝟐𝟐 +𝟐 + 𝟐 𝟒𝒙 = −𝟐𝟎 𝟒 𝟒 𝒙 = −𝟓 1. Solve 𝟑𝒙 − 𝟗 + 𝟕 = 𝟔𝟕 −𝟕 − 𝟕 𝟑𝒙 − 𝟗 = 𝟔𝟎 𝟑𝒙 − 𝟗 = 𝟔𝟎 or 𝟑𝒙 − 𝟗 = −𝟔𝟎 +𝟗 + 𝟗 +𝟗 + 𝟗 𝟑𝒙 = 𝟔𝟗 𝟑𝒙 = −𝟓𝟏 𝒙 = 𝟐𝟑 or 𝒙 = −𝟏𝟕 ► 2. Solve 𝟐𝒙 + 𝟑 + 𝟒 = 𝟐𝟕 −𝟒 − 𝟒 𝟐𝒙 + 𝟑 = 𝟐𝟑 𝟐𝒙 + 𝟑 = 𝟐𝟑 or 𝟐𝒙 + 𝟑 = −𝟐𝟑 −𝟑 − 𝟑 −𝟑 −𝟑 𝟐𝒙 = 𝟐𝟎 𝟐𝒙 = −𝟐𝟔 𝒙 = 𝟏𝟎 or 𝒙 = −𝟏𝟑 1. Write an equation of the line that passes through the points (𝟎, −𝟓) and (𝟑, 𝟒). 𝟒−(−𝟓) • Slope (𝑚)= 𝟑−𝟎 𝒚 = 𝟑𝒙 + 𝒃 −𝟓 = 𝟐 𝟎 + 𝐛 −𝟓 = 𝟎 + 𝒃 −𝟓 = 𝒃 = 𝟗 𝟑 𝒐𝒓 𝟑 𝒚 = 𝟑𝒙 − 𝟓 2. Write an equation of the line that passes through the points (𝟐, 𝟎) and (−𝟐, 𝟔). 𝟔−𝟎 𝟔 𝟑 Slope (𝑚) = = 𝒐𝒓 − 𝟑 𝟎 = − (𝟐) + 𝒃 𝟐 𝟎 = −𝟑 + 𝐛 +𝟑 + 𝟑 𝟑=𝒃 −𝟐−𝟐 −𝟒 𝟐 𝟑 𝒚=− 𝒙+𝟑 𝟐 Solving a Compound Inequality with Or Solve 3x +𝟐 < 𝟏𝟕 or 2x – 8 ≥ 4. Graph the solution. SOLUTION A solution of this inequality is a solution of either of its simple parts. You can solve each part separately. 3𝒙 + 𝟐 < 𝟏𝟕 −𝟐 −2 3x < 𝟏𝟓 3 3 x<𝟓 or or or 𝟐𝒙 − 𝟖 ≥ 𝟒 +𝟖 + 𝟖 2x ≥ 12 2 2 x≥6 0 1 2 3 4 5 6 7 8 Solving a Compound Inequality with And Solve −𝟏𝟑 ≤ -2x + 3 < −7. Graph the solution. SOLUTION Isolate the variable x between the two inequality symbols. −𝟏𝟑 ≤ −2x + 3 < −7 −𝟑 −𝟑 −𝟑 −𝟏𝟔 ≤ −𝟐x < -10 −𝟐 − 𝟐 −𝟐 Write original inequality. Subtract 3 from each expression. Divide each expression by -2. 8 ≥ x >5 𝟓<𝒙≤𝟖 5 6 7 8 9