**Using Averages and Range**

Starter

Main Activity 1

Red

Problems with averages

Five numbers have a mode of 3, a median of 4, a mean of 5 and a range of 6. What are the 5 numbers?

A basketball player has a mean score of 36 points after 10 games. After the next game his mean has fallen to 35 points. How many points did he score in the game?

**L.O. - Compare using the mean and the range, and solve problems using averages and range.**

Two pupils take 10 tests throughout the year. Their percentage scores are given below:

Pupil A - 38, 50, 72, 0, 12, 0, 85, 43, 7, 0

Pupil B - 17, 23, 35, 54, 20, 25, 41, 21, 25, 44

Which pupil do you think did best? Why do you think that?

Comparing

Two pupils take 10 tests throughout the year. Their percentage scores are given below:

Pupil A - 38, 50, 72, 0, 12, 0, 85, 43, 7, 0

Pupil B - 17, 23, 35, 54, 20, 25, 41, 21, 25, 44

Pupil A Mean =

Pupil A Range =

Pupil B Mean =

Pupil B Range =

Comparing

Two pupils take 10 tests throughout the year. Their percentage scores are given below:

Pupil A - 38, 50, 72, 0, 12, 0, 85, 43, 7, 0

Pupil B - 17, 23, 35, 54, 20, 25, 41, 21, 25, 44

Pupil A Mean = 307/10 = 30.7 marks on average.

Pupil A Range = 85 - 0 = 85 marks difference.

Pupil B Mean = 305/10 =

30.5 marks on average.

Pupil B Range = 54 - 20 = 34 marks difference.

Amber

Green

Red

Amber

Green

Range = 6

Mean = 5.875

Range = 0.8 secs

Mean = 10.62 secs

Range = 3

Mean = 6

Range = 7

Mean = 6.5

Problems with averages

Five numbers have a mode of 3, a median of 4, a mean of 5 and a range of 6. What are the 5 numbers?

A basketball player has a mean score of 36 points after 10 games. After the next game his mean has fallen to 35 points. How many points did he score in the game?

3, 3, 4, 6, 9

After 10 games a total 10 x 36 = 360 points; After 11 games a total of 11 x 35 = 385 points. Therefore scored 25 points.

Main Activity 2

Relay competition:

You start with card 1. You answer it and bring

it up to me. If you are right I will give you 3

points if not I will give you back card 1. After that whenever you get it right you get one point.

This then continues through to card 4.

Whichever table gets the most points in the time of the activity wins.

Dice of Ultimate Power

1) Give a key word for the lesson.

2) Summarise one key point for the

lesson.

3) Explain one thing you have learned this

lesson.

4) State one thing you still don't understand following this lesson.

5) Suggest one thing you would like to find out

based on this lesson.

6) Free choice from 1 to 5, or another you make

up.

Question 1 - ........, 3, 3, 3, ........, .......... [any numbers can fill the gaps as long as they are in order.]

Question 2 - 5, 5, 7, 8

Question 3 - If A = 75 then B+C = 135 (because A + B + C = 210)

This means D = 93 (because B + C + D = 228)

This means C and E are both 69 (because C + D + E =

231 and C and E are the same)

This means B = 66 (because B + C = 135)

Question 4 - Let n be the final number of paper. Then:

T + 89 = 68n and T + 57 = 64n.

If we look at the difference between these, that

shows that 32 marks = 4n [32 = 4n].

This gives n = 8 papers.

**Key Examples**

**Activity Answers**

**Activities**

**Worked Example**

**Worked Example**