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Chapter 32: Problem 2

Produce a list of 20 random whole numbers between 1 and 5 using a spreadsheet. If using MS Excel, investigate the RAND() and INT functions. The RAND0 function produces a random number between 0 and 1 , so you will need to multiply by a constant factor to scale your final output appropriately. Copy your test formula(e) to several cells to test empirically whether it works.

Short Answer

Expert verified
Use =INT(RAND()*5) + 1 formula in Excel to generate 20 random numbers between 1 and 5.

Step by step solution

01

Understanding the Functions

The RAND() function in Excel generates a random decimal number between 0 and 1. To convert this into an integer within a specific range, you will need to use the INT() function, which rounds a number down to the nearest whole number.
02

Determine the Scaling Factor

Since you need random whole numbers between 1 and 5, determine an appropriate scaling factor. The range from 1 to 5 is 5 numbers, so you need to multiply the RAND() function by 5 to get a number between 0 and just under 5.
03

Construct the Formula

Use the formula: =INT(RAND()*5) + 1. Here, the RAND()*5 produces a random number between 0 and just under 5, and adding 1 shifts this range to be between 1 and 5.
04

Enter the Formula in Excel

Open MS Excel and select the cell where you wish to start your random number generation. Enter the formula =INT(RAND()*5) + 1.
05

Copy the Formula to Generate Multiple Numbers

Click on the cell with your formula and drag the fill handle (a small square at the bottom-right corner of the cell) down to fill 20 cells. Ensure that each cell now displays a random number between 1 and 5.
06

Verify the Results

Review the cells to ensure they each contain a number between 1 and 5. If each number meets this criteria, your formula has been implemented correctly.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

RAND function
In Excel, the RAND function is a powerful tool for generating random numbers. It works by returning a decimal number that is greater than or equal to 0 and less than 1. This function is particularly useful when you want to simulate randomness, like for creating random data or for statistical sampling.

The beauty of the RAND function is its simplicity:
  • It does not require any arguments.
  • It's as easy as typing `=RAND()` into an Excel cell.
Use cases for RAND are wide and varied, but it's essential to remember that it only generates decimal numbers in its original form. To convert these decimals to integers within a specific range, additional functions like INT are needed.
INT function
The INT function in Excel is used to convert a decimal number into an integer by rounding it down to the nearest whole number. This is particularly useful when you need whole numbers instead of decimals, as in the creation of random integers between specific bounds.

When using the INT function:
  • The syntax is straightforward: `=INT(number)`.
  • It takes a single numeric value as an argument, which is the number you want to round down.
By combining INT with RAND, you can transform a random decimal into a random integer, which is vital for tasks requiring non-decimal randomization, such as generating random whole numbers.
scaling factor
The scaling factor is an important concept when you want to generate random numbers within a specific range using the RAND function. It essentially determines the spread of possible values that your random number can take.

Here's how it works:
  • Decide the range of numbers you want (e.g., 1 to 5).
  • The scaling factor is the size of this range. For 1 to 5, the scaling factor is 5 (since there are 5 possible integers: 1, 2, 3, 4, 5).
  • Multiply the output of RAND by the scaling factor to stretch the number span from 0 to just below 5.
The scaling factor is crucial for adjusting the output of RAND so that it maps correctly to your desired results.
Excel formula
Constructing the correct Excel formula using RAND and INT involves combining these functions in a way that transforms a random decimal number into a random integer within your specified range.

For generating random whole numbers between 1 and 5:
  • Start with: `=RAND()*5` to scale the random decimal between 0 and just below 5.
  • Wrap this in INT: `=INT(RAND()*5)` to round down to the nearest whole number between 0 and 4.
  • Add 1: `=INT(RAND()*5) + 1` to shift the whole range up, perfectly landing you between 1 and 5 inclusive.
This formula is applied in Excel by simply typing it into a cell. Once entered, you can replicate it across multiple cells to provide a list of random numbers, fulfilling whatever specific requirements you have.

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