1 Balance Point of a Data Set

Balance Point of a Data Set

What does the balance point of a

data set represent?

Work with a partner.

● Tape a marker securely to your desk.

● Model the data set 2, 3, 6, 8, 9, 11 by centering quarters on 2 inches, 3 inches, 6 inches, 8 inches, 9 inches, and 11 inches of a 12-inch ruler.

● Carefully place the ruler on top of the marker. Make sure that the coins do not move from their original positions. Try to balance the ruler on the marker. To the nearest half inch, at what value on the ruler is the data balanced?

● Find the mean of the data. What do you notice?

ACTIVITY: Estimating the Balance Point11

The balance point of a data set is the point on a number line where the data distribution is balanced.

STANDARDS OF LEARNING

6.15a

ANDARDSTAA

1234567891 0 1 11 21 31 41 51 61 71 81 92 0 2 0 2 12 22 32 42 52 62 72 82 93 0 CM

1 2 3 4 5 6 7 8 9 10 11 12INCH

Balance Point of a Data Set 2

Use the interactive activity to fi nd the balance point of the data set.

● Enter the least value and greatest value of the data set. Then press the “Populate Data” button.

● Drag the counters to the number line to model the data set.

● Drag the red triangle under the number line until the data is balanced (triangle turns green).

● Find the mean of the data. What do you notice?

ACTIVITY: Using Technology to Find the Balance Point22

3. IN YOUR OWN WORDS What does the balance point of a data set represent? Explain.

3 Balance Point of a Data Set

Use the ruler method in Activity 1 to estimate the mean of the data set.

1. 2, 2, 8, 9, 9 2. 1, 3, 4, 7, 8, 10

3. REASONING Suppose a ruler with several coins is balanced on a marker. What happens when you move some of the coins to the right? the left? Explain how this affects the mean.

Use the interactive activity to fi nd the mean of the data set.

4. 8, 5, 6, 9 5. 0, 1, 2, 3, 4

6. 0, 0, 1, 1, 3, 4 7. 120, 95, 103, 125, 80, 108, 90