Frequency Tables, Stem-and-Leaf Plots, and Line Plots Notes 50 Frequency Tables, Stem-and-Leaf Plots, and Line Plots

Vocabulary Frequency table- a way to organize data into categories or groups. Cumulative frequency- a running total of the frequencies in each category. Stem-and-leaf plot- uses the digits of each number to organize and display a set of data. Each leaf on the plot represents the right-hand digit in a data value, and each stem represents the reamining left- hand digits. Line plot- display of a set of data where each separate piece of data is shown as a dot or mark above a number line.

A frequency table is a way to organize data into categories or groups. By including a cumulative frequency column in your table, you can keep a running total of the frequencies in each category. The frequency of a data value is the number of times it occurs. Remember!

Additional Example 1: Organizing and Interpreting Data in a Frequency Table The list shows the average high temperatures for 20 cities on one February day. Make a cumulative frequency table of the data. How many cities had average high temperature below 59 degrees? 69, 66, 65, 51, 50, 50, 44, 41, 38, 32, 32, 28, 20, 18, 12, 8, 8, 4, 2, 2 February Temperatures in 20 Cities Average Highs Frequency Cumulative Frequency Step 1: Choose a scale that includes all of the data values. Then separate the scale into equal intervals. 0–19 20–39 40–59 60–79

Additional Example 1 Continued The list shows the average high temperatures for 20 cities on one February day. Make a cumulative frequency table of the data. How many cities had average high temperature below 59 degrees? 69, 66, 65, 51, 50, 50, 44, 41, 38, 32, 32, 28, 20, 18, 12, 8, 8, 4, 2, 2 February Temperatures in 20 Cities Average Highs Frequency Cumulative Frequency Step 2: Find the number of data values in each interval. Write these numbers in the “Frequency” column. 0–19 7 20–39 5 40–59 5 60–79 3

Additional Example 1 Continued The list shows the average high temperatures for 20 cities on one February day. Make a cumulative frequency table of the data. How many cities had average high temperature below 59 degrees? 69, 66, 65, 51, 50, 50, 44, 41, 38, 32, 32, 28, 20, 18, 12, 8, 8, 4, 2, 2 February Temperatures in 20 Cities Average Highs Frequency Cumulative Frequency 0–19 20–39 40–59 60–79 7 5 3 Step 3: Find the cumulative frequency for each row by adding all the frequency values that are above or in that row. 7 12 17 20 17 cities had average high temperature below 59 degrees.

Check It Out: Example 1 The list shows the grades received on an English exam. Make a cumulative frequency table of the data. How many students received a grade of 79 or below? 85, 84, 77, 65, 99, 90, 80, 85, 95, 72, 60, 66, 94, 86, 79, 87, 68, 95, 71, 96

A stem-and-leaf plot uses the digits of each number to organize and display a set of data. Each leaf on the plot represents the right-hand digit in a data value, and each stem represents the remaining left-hand digits. 2 4 7 9 3 0 6 Stems Leaves Key: 2|7 means 27

Additional Example 2: Organizing and Interpreting Data in a Stem-and-Leaf Plot The data shows the number of years coached by the top 15 coaches in the all-time NFL coaching victories. Make a stem-and-leaf plot of the data. Then find the number of coaches who coached fewer than 25 years. 33, 40, 29, 33, 23, 22, 20, 21, 18, 23, 17, 15, 15, 12, 17 Step 1: Order the data from least to greatest. Since the data values range from 12 to 40, use tens digits for the stems and ones digits for the leaves.

Additional Example 2 Continued The data shows the number of years coached by the top 15 coaches in the all-time NFL coaching victories. Make a stem-and-leaf plot of the data. Then find the number of coaches who coached fewer than 25 years. 33, 40, 29, 33, 23, 22, 20, 21, 18, 23, 17, 15, 15, 12, 17 Step 2: List the stems from least to greatest on the plot. Stems Leaves The stems are the tens digits. 1 2 3 4

Additional Example 2 Continued The data shows the number of years coached by the top 15 coaches in the all-time NFL coaching victories. Make a stem-and-leaf plot of the data. Then find the number of coaches who coached fewer than 25 years. 33, 40, 29, 33, 23, 22, 20, 21, 18, 23, 17, 15, 15, 12, 17 Step 3: List the leaves for each stem from least to greatest. Stems Leaves The stems are the tens digits. The leaves are the ones digits. 2 5 5 7 7 8 1 2 3 4 1 2 3 3 9 3 3

Additional Example 2 Continued Step 4: Add a key and a title. Stems Leaves 1 2 3 4 5 7 8 9 Number of Years Coached The stems are the tens digits. The leaves are the ones digits. Key: 2 | 1 means 21. 11 coaches coached fewer than 25 years.

The table shows the number of points a player Check It Out: Example 2 The table shows the number of points a player scored during the last ten games of the season. Make a stem-and-leaf plot of the data. In how many games did the player score less than 30 points? 42 Mar 4 46 Feb 20 43 Mar 1 27 Feb 18 31 Feb 27 34 Feb 14 18 Feb 25 36 Feb 7 Points GameDate GameDate Mar 3 Feb 23 32 28

Additional Example 3: Organizing and Interpreting Data in a Line Plot Make a line plot of the data. How many hours per day did Morgan babysit most often? Number of Babysitting Hours in July 6 3 4 8 Wk 4 2 1 5 Wk 3 7 Wk 2 Wk 1 Su S F Th W T M

Additional Example 3 Continued Make a line plot of the data. How many hours per day did Morgan babysit most often? Step 1: The data values range from 0 to 8. Draw a number line that includes this range. 0 1 2 3 4 5 6 7 8

Additional Example 3 Continued Make a line plot of the data. How many hours per day did Morgan babysit most often? Step 1: The data values range from 0 to 8. Draw a number line that includes this range. 0 1 2 3 4 5 6 7 8

Additional Example 3 Continued Make a line plot of the data. How many hours per day did Morgan babysit most often? Step 2: Put an X above the number on the number line that corresponds to the number of babysitting hours in July. X X X X X X X X X X X X X X X X X X X X X X X X X X X X 0 1 2 3 4 5 6 7 8 The greatest number of X’s appear above the number 6. This means that Morgan babysat most often for 6 hours.

Check It Out: Example 3 The hourly rates Morgan got for her last 10 jobs were $6, $6, $8, $7, $8, $9, $6, $10, $8, $6. Make a line plot of the data. What was the most common hourly rate?