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The Bakery Where the Average Misleads

7th grade nonfiction passage about mean and median: 226 words, six questions, an answer key and vocabulary.

7th grade nonfiction mean and median 226 words

The Bakery Where the Average Misleads

Imagine a small bakery with nine people on its payroll. Eight workers each earn $30,000 a year. The owner earns $120,000. A newspaper writer wants to describe how much people at the bakery make, and she has to choose which kind of average to use.

The mean is what most people think of first. To find it, add up all the values and divide by how many there are. The eight workers add up to $240,000, and with the owner's pay the total is $360,000. Dividing by nine people gives a mean of $40,000. That number sounds nice, but not one worker actually earns it. The single large paycheck pulled the mean upward.

The median is a different average. To find it, put the values in order from least to greatest and pick the one in the middle. With nine people, the fifth value is in the middle, and it is $30,000. The median describes the typical worker much better, because it is not dragged around by one unusual value.

Statisticians call a value far from the rest an outlier. When a data set has an outlier, the mean can be misleading, while the median stays steady. Home prices and salaries are often reported with the median for this reason. A careful reader asks which average was used, and a careful writer sometimes reports both so that the full picture is clear.

Questions

  1. How much does each of the eight workers earn in a year? in the text

  2. How do you find the mean of a group of numbers? in the text

  3. What is the mean pay at the bakery? in the text

  4. What is the median pay at the bakery? in the text

  5. Why does the mean sound higher than what the workers really earn? think about it

  6. Why are home prices often reported with the median? think about it

Words to know

payroll
the list of people a business pays
mean
the average found by adding values and dividing
median
the middle value when numbers are put in order
outlier
a value that is far away from the rest
misleading
giving a false idea
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One passage, three levels

The same topic and facts written three ways, so a mixed class can read and talk about one text. Each group’s sheet shows only a shape; the key says which is which.

● Easier · 194 words · Flesch-Kincaid grade 3.5

Picture a small bakery with nine people on its payroll. Eight workers each earn $30,000 a year. The owner earns $120,000. A writer for the newspaper wants to tell how much people at the bakery make. She must pick which kind of average to use.

The mean is what most people think of first. To find it, add all the values. Then divide by how many there are. The eight workers add up to $240,000. With the owner, the total is $360,000. Divide by nine people. The mean is $40,000. That sounds nice, but no worker earns that much. One big paycheck pulled the mean up.

The median is a different average. Put the values in order from least to greatest. Pick the one in the middle. With nine people, the fifth value is in the middle. It is $30,000. The median shows the typical worker better. One odd value does not drag it around.

A value far from the rest is called an outlier. With an outlier, the mean can mislead. The median stays steady. Home prices and salaries are often shown with the median. A careful reader asks which average was used. A careful writer may show both.

▲ This passage · 226 words · Flesch-Kincaid grade 6.4

Imagine a small bakery with nine people on its payroll. Eight workers each earn $30,000 a year. The owner earns $120,000. A newspaper writer wants to describe how much people at the bakery make, and she has to choose which kind of average to use.

The mean is what most people think of first. To find it, add up all the values and divide by how many there are. The eight workers add up to $240,000, and with the owner's pay the total is $360,000. Dividing by nine people gives a mean of $40,000. That number sounds nice, but not one worker actually earns it. The single large paycheck pulled the mean upward.

The median is a different average. To find it, put the values in order from least to greatest and pick the one in the middle. With nine people, the fifth value is in the middle, and it is $30,000. The median describes the typical worker much better, because it is not dragged around by one unusual value.

Statisticians call a value far from the rest an outlier. When a data set has an outlier, the mean can be misleading, while the median stays steady. Home prices and salaries are often reported with the median for this reason. A careful reader asks which average was used, and a careful writer sometimes reports both so that the full picture is clear.

■ Harder · 247 words · Flesch-Kincaid grade 9

Imagine a modest neighborhood bakery with nine people on its payroll. Eight of the employees each earn $30,000 a year, while the owner earns $120,000. A newspaper reporter hoping to describe how much people at the bakery make must decide which kind of average will present the most honest picture.

The mean is the measure that most people think of first. To calculate it, you add together all of the values and then divide by how many values there are. The eight employees contribute $240,000, and with the owner's salary the total reaches $360,000. Dividing by nine people produces a mean of $40,000. That figure sounds respectable, but not a single employee actually earns it, because the one exceptionally large paycheck has pulled the mean upward.

The median is a different kind of average. To find it, you arrange the values from least to greatest and select the one in the middle. With nine people, the fifth value sits in the middle, and it is $30,000. The median describes the typical employee far more accurately, since it is not dragged around by a single unusual value.

Statisticians use the word outlier for a value that lies far from all the others. When a data set contains an outlier, the mean can be misleading, whereas the median remains steady. For this reason, home prices and salaries are frequently reported using the median. A thoughtful reader asks which average was used, and a thoughtful writer sometimes reports both so that the complete picture is clear.

Download as one PDF

How to use it

  1. Press Read it big (or B) to put the text on the projector, or Full screen (F) to fill the whole screen.
  2. Ask the questions one at a time and use Show answer when the class has decided. A shows or hides every answer.
  3. Print student copy for the class, or Print with answers for yourself.

Ideas for class

  • Before reading, put payroll, mean, median, outlier and misleading on the board with their meanings from the Words to know section and have students predict what the text will be about.
  • Read it aloud once while students follow along, then have them reread it alone or with a partner. At a calm 100 words a minute it takes about 2 minutes to read aloud.
  • Use the Read it big button (or B) to put the text on the projector, and Show answer on one question at a time so the class commits to an answer first.
  • Question 5 asks the reader to infer. Ask students to point to the words in the passage that led them to their answer.
  • Ask students to write one question the passage did not answer, then look for the answer in a book or on a classroom screen.
  • Print the student copy for independent work and keep the answer-key copy for yourself.

Related

Questions

What reading level is "The Bakery Where the Average Misleads"?

It was written for 7th grade. It has 226 words and works out to a Flesch-Kincaid grade level of about 6.4. That is a formula's estimate from sentence length and syllables, and it is not a Lexile or a guided reading level, so check it against your students.

What do the questions ask?

There are six. 4 ask for something the text says directly and 2 ask the reader to work something out from clues. Each has an answer in the key, and the answers are written as a teacher would accept them, not as the only possible wording.

How long does it take to read?

About 2 minutes read aloud at 100 words a minute. For a one-minute fluency check, paste it into the fluency timer and use the word count.

Can I print it?

Yes. Print student copy gives the passage, the questions with lines to write on, and the word meanings. Print with answers gives the same page with the answers filled in. Both are made in your browser.

Is this passage from a published book?

No. It was written for Peabody Teach, so there is no book to buy and no login to read it.

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