Algebra Room 424 Ms. Miller

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Please sign in next to your name on the sheet by the door.

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I have pencils, pens, paper, if you need it.

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I will be available in my room from 12:00 - 12:30 for tutoring on Tuesdays and Thursdays if you ever want extra help. (PLEASE LET ME KNOW AHEAD OF TIME)

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The day’s lesson and the homework will be posted to my website by the end of each day.

www.mrsmillersmathtutoring.com

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Always feel free to email me with any questions or concerns.

jmiller1@camdencc.edu

Warm Up: You have 10 minutes to work on these problems. Then, we will go over them.

Workbook page 29

HOMEWORK

Find the median.

Find the mode.

Solve.

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9. The following data shows the number of sales made in a month by 8 out of 9 salespeople.

45 34 31 48 37 43 32 42

The 9^th employee made 66 sales in that month. By how much does the mean change when the 9^th value is added?

10. Explain. The data below gives the margin of victory for a high school football team’s games in a season.

3 7 21 14 3 17 30 3

Do you think the mean, median, or mode is the most reliable typical value for the data? Explain your reasoning.

The average before: 39

The average after: 42

Mean: 12.25

Median: 10.5

Mode: 3

This is your interpretation of the data.

What do YOU think?

3 3 3 7 14 17 21 30

HOMEWORK

Using Typical Values

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When news sources report the results of a survey or study, they don’t usually tell you all of the data.

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Instead, they might sum up the study with a typical value.

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You must use your knowledge of mean, median, and mode to interpret the information.

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TIPS:

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Average = Mean

Be careful – Outliers can make the mean misleading

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Median = Middle

Outlier don’t have a big effect on the median

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Mode = Most

Useful when you care what is popular or frequent.

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Use your knowledge of mean, median, and mode to answer the following questions.

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1. In Mr. Bound’s class, 1 student scores a 76 on a test, 10 students scored above 76, and 10 students scored below 76. What typical value does a score of 76 represent?
1. Mean
2. Median
3. Mode

2. The manager at a toy store wants to reorder the items that sell the best. Which typical value should he use to decide which items to reorder?
1. Mean
2. Median
3. Mode

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3. Explain You are researching housing prices. You can afford a house that will sell for about $150,000. You know the mean, median, and mode for a certain neighborhood. Which typical value would be the most helpful in deciding whether you can afford a house in this neighborhood? Explain your answer.

Use your knowledge of mean, median, and mode to answer the following questions.

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Use your knowledge of mean, median, and mode to answer the following questions.

4. An office poll asks employees how many cups of coffee they drink in a week. The mean of the data is 15, but the median is 21. Which of the following is true?
1. A few people drink much fewer than 21 cups of coffee a week
2. A few people drink much more than 21 cups of coffee a week
3. Most people drink between 15 and 21 cups of coffee a week

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5. Out of the 25 students in a 5^th grade class, 22 are between 49 and 51 inches tall. Three students are 59 inches tall. Which of the following must be true?
1. The median is higher than the mean
2. The mean is higher than the median

6. Explain The mean salary for NBA basketball players is about $5 million a year. The median salary for NBA players is about $2.5 million a year. Why do you think the two typical values are so different?

Use your knowledge of mean, median, and mode to answer the following questions.

Sometimes line graphs display the mean, median, or mode of a data set.

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These graphs show how typical values change over time.

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USING TYPICAL VALUES TO INTERPRET GRAPHS

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Example: This graph shows the U.S. median age from 1970 to the estimated value for 2020. What can you conclude about the U.S. population?

You can see that the median age has increased from 1970 to present.

The median is the middle value. If the median age in 2010 is 37, that means there is an equal number of people younger than 37 and older than 37.

If the median age is increasing, you can conclude that the population is getting older.

Use the bar graph for problems 7 & 8.

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The graph shows the average high temperature in a forest from March to June. Researchers recorded the high temperature for each day in a month and calculated the average of those values.

7. Which typical value does this graph use?

Use the circle graph for problems 9 & 10.

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The graph shows the breakdown of dress sales at a boutique over the weekend.

9. Which sizes represent the mode of the data?

10. Explain Can you determine from the graph what the median size would be? Explain your answer.

Numbers 9 & 10 are HOMEWORK

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Weighted Averages

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Sometimes, the values in a data set may not be equally important. For example, a final exam might count as two tests.

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If you were finding your average in the class, your final exam score would be worth more than your other scores.

When some value in a data set are worth more than others, you must find the weighted average.

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Finding a Weighted Average

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EXAMPLE: Aparna’s average for the first 4 tests is 80. Her score on the fifth test is 90. What is her average in the class?

You might be tempted to say 85 because it is the mean of 80 and 90. Look at the diagram.

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Note that 80 represents 4 tests, but 90 only represents 1 test.

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You must find the weighted average.

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Finding a Weighted Average

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EXAMPLE: Aparna’s average for the first 4 tests is 80. Her score on the fifth test is 90. What is her average in the class?

Step 1

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Multiply each score by the weight.

(How many times you use it)

Then add.

Step 2

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Divide by the number of values, 5 tests.

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Some averages are calculated by assigning percentages to different categories.

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These percentages must add up to 100%.

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Since the percentages represent one whole, you DO NOT need to divide at the end.

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Step 1

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Multiply Jeff’s scores by the percent weights.

Step 2

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Add.

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1. On a recent road trip, Cesar averaged 65 mph for the first 4 hours and 80 mph for the final 6 hours. What was his average speed for the entire trip?

74 mph

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2. An online food critic rates restaurants based on four criteria. She assigns the following weights to the categories. Blossom Café receives the following:

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8 for Taste, 7.8 for Presentation, 8.4 for Service, and 8.2 for Atmosphere.

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What is Blossom Café’s total weighted average?

8.1 average score

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3. The table shows how many hours Yeri worked each day during the past three months. What is the average number of hours Yeri worked per day over the past three months? Round your answer to the nearest tenth.

(Hint: Treat the number of days as the weight)

7.9 hours

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4. In the first 10 games of the season, a quarterback has a 60% pass completion rate. In the last 5 games, his pass completion rate is 78%. What is his pass completion rate for the entire season?

5. At a gymnastics meet, Michelle receives 152 points for execution and 110 points for artistry. Execution makes up 65% of her total score, while artistry makes up 35% of her score. What is Michelle’s final score?

HOMEWORK

HOMEWORK

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6. Mr. Reyes gives his students the following circle graph to explain their final grade.

Christian receives a 75 for tests, a 78 for participation, an 85 for homework, an 80 for essays, and a 90 for the final project. What is his final grade in the class, rounded to the nearest whole number?

HOMEWORK

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7. Paul buys two suits for $175 each at one store and three suits for $150 each at a different store. How much did Paul pay on average per suit?

8. After the first three months of the season, a baseball player’s batting average is 0.300. After another month, his average for the four months is 0.275. Which of the following is most likely?

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• He did not play the last month
• He batted about 0.200 the last month
• He batted about 0.300 the last month
• He batted about 0.350 the last month

HOMEWORK

HOMEWORK

Tonight’s homework:

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Page 33, numbers 9 and 10

Page 35, numbers 4 - 8