# How Many Numbers Can You Remember?

## Abstract

Are you good at remembering addresses and phone numbers? How many numbers do you think you can remember? Try this experiment to test your digit span, the maximum number of digits that you can remember.## Summary

Sara Agee, Ph.D., Science Buddies

## Objective

In this experiment, you will test how many digits people can remember.

## Introduction

How good is your **memory**? Are you good at remembering phone numbers? Most people do not even memorize phone numbers anymore, and instead program them into their phones' address book. There is a limit to the number of numbers, or **digits**, that most people can remember. The longest string of numbers that anyone has ever memorized is for the number pi (3.14159265...). Akira Haraguchi from Japan set a new world record by memorizing the first 100,000 digits on Oct. 3rd, 2006. That's a lot of digits!

Our memory is a function of our brain, which processes and stores information from the world around us using our five senses: sight, sound, smell, taste, and touch. The brain integrates these experiences into a memory. For some people, certain senses create stronger memory than other senses. There are even people who never forget a smell, and become perfume makers!

In this experiment, you will test the memory of your participants. You will have them remember **sequences** of numbers that they hear you read. You will test them and compare how many they get correct. This will test the **digit span** of your volunteers. How many numbers will they remember?

### Terms and Concepts

- Memory
- Digits
- Sequence
- Digit span
- Random numbers
- Frequency

### Questions

- How many digits can people remember?
- Will most people remember the same number of digits?
- Are there other factors affecting digit memory, like age or gender?

### Bibliography

- Wikipedia contributors, 2017. Memory Span, Wikipedia, The Free Encyclopedia. Retrieved on March 7, 2017.
- Wikipedia contributors, 2017. Memory, Wikipedia, The Free Encyclopedia. Retrieved on March 7, 2017.
- Haahr, M. 2017. Random Integer Generator random.org. Retrieved on March 7, 2017.

## Materials and Equipment

- Computer, smartphone or tablet with internet connection
- Index cards
- Volunteers
- Lab notebook

## Experimental Procedure

- In this experiment, you will need to write sequences of digits on different index cards. The first card will have two digits, the next card will have three digits, and so on. To select the digits, you should use a
**random number**generator. A random number is a number that is generated by a random (uncontrollable) process like rolling a die. You should avoid just "picking" the numbers yourself, because you might accidentally introduce a pattern that your volunteers could recognize. Search online for "random number generator" to find one. - On the first index card, write a sequence of two random digits. How you generate the digits will depend on the random number generator you are using. For example, you could set it to generate a one-digit random number from 0–9, and generate the digits one at a time. Or, you could set it to generate a two-digit random number (from 00–99) and generate both digits at once.
- Repeat step 2 for index cards with 3, 4, 5, 6, 7, 8, 9, and 10 digits. Stack the index cards in order of the increasing number of digits, to keep them organized for your experiment.
- Make a data table like this one in your lab notebook. You will use it to keep track of the highest number of digits each volunteer could remember:

Volunteer Info: | Highest Number of Digits Remembered: | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Name | Age | Gender | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

- Explain to your first volunteer that you will read them a series of numbers slowly, and then you would like them to repeat the numbers back to you in the same order.
- Beginning with the 2-digit card, read the numbers slowly and let the volunteer respond. If they get the numbers right, put a check in that box in your data table and then move on to the 3-digit card. Repeat this process until they get a number wrong, then stop and move on to the next volunteer. Pay attention to these important notes during your experiment:
- When you read the numbers, read them one digit at a time. For example, for the number "326" you would say "three two six," not "three hundred and twenty six."
- Make sure you test your volunteers one at a time, while the other volunteers are not in hearing range. Other volunteers may gain an advantage if they hear the numbers repeated over and over.
- Make sure your volunteers cannot see the index cards. No cheating!

- Repeat steps 5–6 for each of your remaining volunteers. You will need to have a lot of participants for this study, so gather data from as many people as you can! The Science Buddies resource, How Many Survey Participants Do I Need?, will show you how to figure out how many respondents you need to recruit in order to achieve your desired level of confidence.
- When you are done, count up the total number of people who got each score on the test and make a frequency table:

Score | Number of participants with this score | Percentage of participants with this score |

0 | ||

1 | ||

2 | ||

3 | ||

4 | ||

5 | ||

6 | ||

7 | ||

8 | ||

9 | ||

10 |

- Calculate the percentage of people who received each score. Do this by first adding the total number of participants for each column, then divide the number of people receiving the score by the total number of participants in your study.
- Analyze your data by making a histogram. On the left side of the graph (y-axis), write a scale for the percentage of people from zero to 100%. On the bottom of the graph, write a scale for the number of correct digits remembered from zero to ten. Then draw your results on the graph. How many digits could most people remember? Could some people remember more than others? See the Make It Your Own section for more ideas about how to analyze your data.

## Ask an Expert

## Variations

- Since you collected data on your participants, you can see if memory is linked to another factor, like gender. Just redo the table in step 17 to include the gender of the volunteers (male vs female) by making two columns, and calculating the results for each gender separately. Do boys or girls have a better memory?
- To test age, you will need to make a more complex table for analysis. Break up your participants into age groups, and then make a separate column for each age group. Do young people or old people have a better memory?
- For a more advanced project, you can evaluate your data using statistics. Calculate the standard deviation and margin of error of your experiment. Then perform a t-test to see if your results are statistically significant.
- Make multiple cards with each number of digits (for example, 10 cards with two digits, 10 cards with three digits...) and test each volunteer with all 10 cards for each number of digits. Instead of tracking a simple yes/no response (checking the box for whether the volunteer remembered a single number correctly), track what percentage of the cards each volunteer can remember for each number of digits. How does the percentage change as the number of digits increases?
- Do the results of the experiment change if you let the volunteers see the card instead of reading it out loud to them? What if you have them write down their responses instead of saying them out loud?

## Careers

If you like this project, you might enjoy exploring these related careers:

## Related Links

## Cite This Page

General citation information is provided here. Be sure to check the formatting, including capitalization, for the method you are using and update your citation, as needed.#### MLA Style

*Science Buddies*, 20 Nov. 2020, https://www.sciencebuddies.org/science-fair-projects/project-ideas/HumBeh_p020/human-behavior/how-many-numbers-can-you-remember. Accessed 17 May 2022.

#### APA Style

*How Many Numbers Can You Remember?*Retrieved from https://www.sciencebuddies.org/science-fair-projects/project-ideas/HumBeh_p020/human-behavior/how-many-numbers-can-you-remember