Reporting Frequency

Reporting Frequency

Frequency Tables Histograms

Reporting Frequency:Frequency Tables and HistogramsReview: Stem-and-Leaf Plots, and Line Plots

Course 2

Warm Up

Problem of the DayLesson Presentation

Warm Up

Jason deposits $200 in an account that earns 3.6% simple interest. How long until the total amount $300.

Course 2

Almost 14 years

Problem of the DayBooks A, B, C, and D are on the bookshelf. A is between C and B. B is between A and D. D is not on the right. What is the order of the books from right to left?

D, B, A, C

Course 2

Learn to organize and interpret data in frequency tables and histograms.Review organizing data in stem-and-leaf plots, and line plots.

Vocabularyfrequency tablecumulative frequencyhistogramstem-and-leaf plotline plot

A stem-and-leaf plot can be used to show how often data values occur and how they are distributed. Each leaf on the plot represents the right-hand digit in a data value, and each stem represents left-hand digits.

2 4 7 93 0 6

Stems Leaves

Key: 2|7 means 27

Things we know: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

Example 1: Organizing and Interpreting Data in a Stem-and-Leaf Plot

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.

Example 1 Continued

Step 2: List the stems from least to greatest on the plot.

Stems Leaves1234

The stems are the tens digits.


Step 3: List the leaves for each stem from least to greatest.

Stems Leaves1234


2 5 5 7 7 80 1 2 3 3 93 30

The leaves are the ones digits.


Example 1 Continued

Step 4: Add a key and a title.


Stems Leaves

1234

2 5 5 7 7 80 1 2 3 3 93 30


Number of Years Coached

Key: 2 | 1 means 21.

11 coaches coached fewer than 25 years.

Example 1 Continued

The list shows the number of times each soccer player can bounce the ball on their knee. How many soccer players can bounce the ball more than 36 times.55, 60, 33, 30, 23, 45, 28, 41, 62, 29, 35, 40, 43, 37, 68, 30, 61, 27, 38, 41

Your Turn: Example 2

Step 1: Order the data from least to greatest. Since the data values range from 23 to 68, use tens digits for the stems and ones digits for the leaves.

Your Turn: Example 2 Continued

Step 2: List the stems from least to greatest on the plot. Stems Leaves

23456




Stems Leaves23456

Step 3: List the leaves for each stem from least to greatest.


3 7 8 90 0 3 5 70 1 1 3 550 1 2 8

8




Step 4: Add a key and a title.


Stems Leaves23456

3 7 8 90 0 3 5 70 1 1 3 550 1 2 8

8

Number of times a Soccer Player can bounce the ball on their knee

Key: 4 | 0 means 40.

12 soccer players can bounce the ball on their knee more than 36 times.


Make a line plot of the data. How many hours per day did Morgan babysit most often?

Example 3: Organizing and Interpreting Data in a Line Plot

M T W Th F S SuWk 1 0 6 4 6 5 8 2Wk 2 2 7 7 7 0 6 8Wk 3 0 6 8 5 6 1 2Wk 4 4 8 4 3 3 6 0

Number of Babysitting Hours in July

Make a line plot of the data. How many hours per day did Morgan babysit most often?

Example 3 Continued

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

DAY 2 Period 3

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.

0 1 2 3 4 5 6 7 8

XXXX

X

XXX XX

XXX XX

XXXXXX

XXX

XXXX

The greatest number of X’s appear above the number 6. This means that Morgan babysat most often for 6 hours.

Example 3 Continued

Make a line plot of the data. How many slices of pizza did most people eat?


2 4 1 2 5 3 10 4 3 2 5 3 24 6 1 4 2 2 5

Number of Slices eaten per Person

Example 4 Continued

Step 1: The data values range from 0 to 6. Draw a number line that includes this range.

0 1 2 3 4 5 6

Make a line plot of the data. How many slices of pizza did most people eat?

0 1 2 3 4 5 6

Make a line plot of the data. How many slices of pizza did most people eat?Step 2: Put an X above the number on the number line that corresponds to the number slices of pizza eaten per person.

X

XXX

XXXXXX

XXX

XXXX XX

XX

The greatest number of X’s appear above the number 2. This means that most people ate 2 slices of pizza.

Example 4 Continued

A frequency table is best used to keep track of and

organize data!

We can even use them to help keep up with data as we are conducting our surveys!

A frequency table is a way to organize data into categories or groups. It lists each item in a data set with the number of times it occurs.

By including a cumulative frequency column in your table, you can keep a running total of the frequencies in each category.

# of Cats Tally Frequency

0 |||| 5

1 ||||| | 6

2 ||| 3

3 or more

| 1

A frequency table contains 3 columns.

# of Cats in Homes

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

Example 5: Organizing and Interpreting Data in a Frequency Table

February Temperatures in 20 CitiesAverage

HighsFrequency Cumulative

FrequencyStep 1: Choose a scale that includes all of the data values. Then separate the scale into equal intervals.

0–1920–3940–5960–79

DAY 2 Period 2, 1


Example 5 Continued

Step 2: Find the number of data values in each interval. Write these numbers in the “Frequency” column.



Frequency7553

0–1920–3940–5960–79


Example 5 Continued

Step 3: Find the cumulative frequency for each row by adding all the frequency values that are above or in that row.



Frequency0–19

20–3940–5960–79

7553

7121720

17 cities had average high temperature below 59 degrees.


English Exam GradesGrades Frequency Cumulative

Frequency60–6970–7980–8990–99

Step 1: Choose a scale that includes all of the data values. Then separate the scale into equal intervals.

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



Step 2: Find the number of data values in each interval. Write these numbers in the “Frequency” column.


Frequency60–6970–7980–8990–99

4466


Step 3: Find the cumulative frequency for each row by adding all the frequency values that are above or in that row.


Frequency60–6970–7980–8990–99

4466

48

1420

8 students received grades of 79 or below.


What is a Histogram?

• A histogram is a bar graph with no spaces between the bars. The height of each bar shows the frequency of data within that interval. The intervals of a histogram are of equal size and do not overlap.

Period 3 Day 3

Histogram

10

9

8

7

6

5

4

3

2

1

10-Jan 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 90-99

Freq

uenc

y

Test Scores

Class Test ScoresExample 7

95 flashlights are tested until they fail. The table gives the times taken ( hours ) until failure.

Time to failure (hours)

0-19 20-29 30-39 40-44 45-49 50-59 60-89

Number of components

5 8 16 22 18 16 10

Find 2 or more things wrong with the histogram which represents the data in the table.

HistogramsExample 8

Answer:

Time to failure (hours)

0-19 20-29 30-39 40-44 45-49 50-59 60-89

Number of components

5 8 16 22 18 16 10

• There is no title.

• There are no units on the x-axis.

Histograms

Time taken for 95 components to fail

Time to failure (Hours)

Example 8 Continue

Histogram – a bar graph that gives the frequency of each value. • In a histogram, the horizontal axis is like a number line divided into equal widths.• Each width represents a data value or range of data

values. • The height of each bar indicates the frequency of that data value or range of data values.

Example 9

*Ex 10. The given data shows the # of people in 24 vehicles that passed a designated checkpoint.

1, 4, 1, 2, 2, 1, 3, 1, 3, 2, 2, 6, 4, 2, 1, 1, 2, 4, 3, 1, 2, 4, 2, 3.

a.) Make a frequency table for these data. b.) Make a histogram from the frequency table.

# Frequency123456

*Ex11. Use the relative frequencies given to estimate the probability that a randomly selected customer will rent a canoe for 5 or more hours.

Question: What % rented a canoe for 5, 6, 7, and 8 hours?

Hours Frequency Relative Frequency

1 3 3/30 = 0.10 = 10%

2 10

3 7

4 4

5 3

6 1

7 1

8 1

Total 30

Histogram

• Histograms are used to show the frequency of data.

• Very similar to bar graphs, but use intervals on the X axis.

• Bars do touch.

• Histograms have a title.

• Histograms have two axes which are labeled.

NOW LET US GET THAT PROJECT DONE

Frequency Tables Histograms

Reporting Frequency

Documents

Transcript of Reporting Frequency