Rounding Numbers and Statistics

Rounding Numbers in Statistics

Introduction

  • In statistics, numerical values are often approximations obtained through rounding.
  • Rounding simplifies numbers to a specific place value.

Steps for Rounding

  1. Identify the Rounding Place Value:
    • Determine the place value to which you are rounding (e.g., whole number, hundredths place, thousandths place).
    • Underline or highlight the digit in this place value.
  2. Examine the Digit to the Right:
    • Look at the digit immediately to the right of the digit you're rounding.
  3. Rounding Rules:
    • Round Up: If the digit to the right is 5 or greater, add 1 to the underlined digit.
    • Round Down: If the digit to the right is 4 or less, leave the underlined digit as it is.
      • Note: "Rounding down" means the value of the number becomes smaller or stays the same.
  4. Adjusting Subsequent Digits:
    • Whole Numbers: Digits to the right of the rounding place value become zeros.
    • Decimal Place Values: Digits to the right of the rounding place value are dropped.
  5. Impact on Value:
    • Rounding down makes the value of the number smaller or stays the same.
    • Rounding up makes the value of the number slightly larger.

Examples

Example 1: Rounding to the Nearest 100,000
  • Round 12,682,100.23 to the nearest 100,000.
  • The digit in the 100,000s place is 6.
  • The digit to the right (8) is 5 or higher, so we round up.
  • Result: 12,700,000 (digits to the right become zeros).
Example 2: Rounding to the Nearest Whole Dollar
  • Round 9,999.983 to the nearest whole number (ones place).
  • The digit in the ones place is 9.
  • The digit to the right (9) is 5 or higher, so we round up.
  • Since 9 rounds up to 10, carry over the 1 to the next digit. This carry-over continues through all the 9s.
  • Result: 10,000
Example 3: Rounding to the Nearest Cent
  • Expressing money to two decimal places means rounding to the hundredths place.
  • Round $5.699
  • The digit in the hundredths place is 9.
  • The digit to the right (9) is 5 or higher, so we round up.
  • Since 9 rounds up to 10, carry the 1 over to the 6.
  • Result: $5.70
Example 4: Rounding to the Hundredths Place
  • Round 0.437 to the hundredths place.
  • The digit in the hundredths place is 3.
  • The digit to the right (7) is 5 or higher, so we round up.
  • Result: 0.44
Example 5: Rounding to the Thousandths Place
  • Round 0.5896 to the thousandths place.
  • The digit in the thousandths place is 9.
  • The digit to the right (6) is 5 or higher, so we round up.
  • In this Case think of 589 rounding up like 590.
  • Since 9 rounds up to 10, carry the 1 over to the 8.
  • Result: 0.590
Example 6: Rounding to the Tenths Place
  • Round 0.99 to the tenths place.
  • The digit in the tenths place is 9.
  • The digit to the right (9) is 5 or higher, so we round up.
  • Since 9 rounds up to 10, carry the 1 over to the 0.
  • Result: 1.0