## Averages - Due 14th June, 23:59 HOL time.

Please send all your work to hol.mathematics@gmail.com.

Send Homework and Extra Credit together or separately, whichever is easier for you.

Please put Averages - HOL ID in the subject line.

Remember to include your HOL username, ID and House in the main body of your email.

Do not send attachments as they will not be opened.

Send Homework and Extra Credit together or separately, whichever is easier for you.

Please put Averages - HOL ID in the subject line.

Remember to include your HOL username, ID and House in the main body of your email.

Do not send attachments as they will not be opened.

## Homework

**Definition Match (4 points plus one bonus question)**Below are four definitions of the mean, median, mode and range but they're not in the correct order. Match the definition to the correct term.

1. Add up all the numbers and divide by how many there are.

2. The most common value.

3. Biggest value minus smallest value.

4. The middle number.

Bonus point: The bottom definition is missing a key part. What is it?

**Averages calculations (16 points, 1 point each)**For the four sets of data below calculate the mode, the median, the mean and the range.

A) 1, 2, 2, 2, 3

B) 1, 5, 7, 9, 11, 15

C) 4, 2, 8, 9, 12, 4, 6

D) 19, 25, 10, 18, 6, 18, 19, 29

**Real Life Averages (9 points, 3 points each)**## Extra Credit

__Short Answer Questions (10 points, 2 points each)__1. Which average would you use to find the least popular snack in your class?

2. To find an average for 34, 64, 37, 54, 242, 51, 45, which would be the most sensible average to choose and why?

3. If I have the data 14, 34, 36, 56, 59, 68, which averages

__are not changed__if I change the 68 to 88?

4. In the above question, what happens to the range? Does it change or stay the same?

5. Which measure would you recommend a shop keeper to use to find the best sizes of shoe to stock and why?

__Comparing data (5 points)__Please write your conclusion in full sentences, using the example given in the lesson to help you. Remember there is no one right or wrong answer here but you must include any values you calculate with your response. You should consider the mean and the range before making your decision

Steven and Tanya are sweet packers. The number of sweets in the last 7 bags they packed are:

Steven: 57, 60, 65, 68, 67, 63, 54

Tanya: 56, 58, 67, 62, 58, 60, 59

If you were the customer buying the bag of sweets, would you prefer to have a back packed by Steven or Tanya? Why?

**Investigation - Reaction Time (15 points)**I would like you to do an investigation to see who has quicker reaction time... you or a friend/relative. It would be good if you could pick someone who is in a different age range to you but I understand that is not always possible so anyone who is willing to take part will do. (A parent or son/daughter would be perfect, a grandparent would be even more interesting if they're willing!)

__Part 1 - The prediction__

__(2 points)__

Before carrying out your investigation I want you to predict who you think will have faster reaction times, you or your friend/relative. Tell me a little about the person you have chosen to take part and yourself. You do not need to give me your exact ages, a range will do (eg teenage, 20's, over 70)

__Part 2 - The test (5 points)__

Both you and your friend/relative need to visit this website. Click on the star to make it vanish and then click again when it reappears. In the table underneath you will have your reaction time given in milliseconds, measuring how long it took you to click once the star had appeared. A smaller number means that you had a quicker reaction. You do not need to change any of the setting options on the left hand side. Each of you needs to complete the test 10 times (you can have a couple of practise goes before you start if you wish) and you need to record your scores. Please send a list of your times or a screenshot clearly showing them along with your assignment.

EDIT: Alternative reaction timers can be found HERE, HERE and HERE for those who are having problems with the link above.

__Part 3 - The calculations (4 points)__

For each of your times, calculate the mean, mode, median and range. This means you have 8 calculations to do. Do not put your scores together as that will not give you any meaningful data to comment on.

__Part 4 - The conclusion (4 points)__

Write a conclusion, using the comparing data part of the lesson as a guide, stating who you have found to have quicker reaction times. Make sure you back up your answer with the maths you did in part 3. Was your prediction correct? Why do you think that person's reactions were quicker?