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The Million Dollar House That Fooled the Mean

5th grade nonfiction passage about mean, median and outliers: 212 words, six questions, an answer key and vocabulary.

5th grade nonfiction mean, median and outliers 212 words

The Million Dollar House That Fooled the Mean

Theo was making a poster about the five houses on his street. All five had been sold in the same year. Four of them sold for $200,000, $210,000, $220,000, and $230,000. The fifth was a huge house, and it sold for $1,000,000.

Theo wanted a single number that would show what a typical house on his street costs. First he tried the mean. To find the mean, you add up all the numbers and divide by how many there are. The total was $1,860,000, and dividing by 5 gave $372,000. Theo frowned, because not one house on his street cost anywhere near that much. In fact, four of the five had sold for much less.

His teacher recommended the median instead. To find the median, you line the numbers up from smallest to largest and pick the one in the middle. Theo's middle number was $220,000. That number described the street much more honestly.

The giant house is called an outlier, which is a number far away from the others. An outlier can pull the mean up or down a lot, but it hardly moves the median. If the big house had sold for $250,000, the mean would have been $222,000, very close to the median. Theo learned that both numbers are useful, but he must think about which one tells the truth.

Questions

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

  2. What was the mean of the five house prices? in the text

  3. How do you find the median? in the text

  4. What is an outlier? in the text

  5. Why did the mean not describe a typical house on Theo's street? think about it

  6. What would have happened to the mean if the big house had sold for $250,000? think about it

Words to know

mean
the number you get when you add everything and divide by how many
median
the middle number when a list is put in order
outlier
a number that is far from the rest
typical
usual, or like most of the others
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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 · 188 words · Flesch-Kincaid grade 1.7

Theo was making a poster about the five houses on his street. All five were sold in the same year. Four sold for $200,000, $210,000, $220,000, and $230,000. The fifth was a huge house. It sold for $1,000,000.

Theo wanted one number to show the price of a house on his street. First he tried the mean. To find the mean, you add all the numbers. Then you divide by how many there are. The total was $1,860,000. Divide by 5 and you get $372,000. Theo frowned. No house on his street cost that much. Four of the five cost less.

His teacher told him to try the median. To find the median, you put the numbers in order from smallest to largest. Then you pick the middle one. Theo's middle number was $220,000. That fit his street much better.

The giant house is an outlier. An outlier is a number far from the others. It can pull the mean way up, but it hardly moves the median. If the big house had sold for $250,000, the mean would be $222,000. That is close to the median. Theo learned that he must think about which number tells the truth.

▲ This passage · 212 words · Flesch-Kincaid grade 4

Theo was making a poster about the five houses on his street. All five had been sold in the same year. Four of them sold for $200,000, $210,000, $220,000, and $230,000. The fifth was a huge house, and it sold for $1,000,000.

Theo wanted a single number that would show what a typical house on his street costs. First he tried the mean. To find the mean, you add up all the numbers and divide by how many there are. The total was $1,860,000, and dividing by 5 gave $372,000. Theo frowned, because not one house on his street cost anywhere near that much. In fact, four of the five had sold for much less.

His teacher recommended the median instead. To find the median, you line the numbers up from smallest to largest and pick the one in the middle. Theo's middle number was $220,000. That number described the street much more honestly.

The giant house is called an outlier, which is a number far away from the others. An outlier can pull the mean up or down a lot, but it hardly moves the median. If the big house had sold for $250,000, the mean would have been $222,000, very close to the median. Theo learned that both numbers are useful, but he must think about which one tells the truth.

■ Harder · 226 words · Flesch-Kincaid grade 6.2

Theo was putting together a poster about the five houses on his street, all of which had been sold during the same year. Four of them sold for $200,000, $210,000, $220,000, and $230,000. The fifth was an enormous mansion, and it sold for a startling $1,000,000.

Theo wanted a single number that would represent what a house on his street costs. At first he calculated the mean. To find the mean, you add up all of the numbers and then divide by how many numbers there are. The total came to $1,860,000, and dividing by 5 gave him $372,000. Theo frowned, because not one house on his street cost anywhere near that much. In fact, four of the five had sold for less.

His teacher recommended that he try the median instead. To find the median, you arrange the numbers from smallest to largest and select the one in the middle. Theo's middle number was $220,000, and that figure represented his street far more honestly.

The enormous house is known as an outlier, which means a number that lies far away from all the others. An outlier can drag the mean sharply upward or downward, yet it barely moves the median. Had the mansion sold for only $250,000, the mean would have been $222,000, very close to the median. Theo realized that both numbers are valuable, but a careful person must decide which one tells the truth.

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 mean, median, outlier and typical 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 Million Dollar House That Fooled the Mean"?

It was written for 5th grade. It has 212 words and works out to a Flesch-Kincaid grade level of about 4.0. 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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