I know some of you have begun extra work towards your projects outside of school. Remember that if you plan to do something, share this with your group so that they are aware what is going on and are in agreement with you. Don't forget that if you continue with your ideas / experiment with making prototype products / sourcing materials / speaking to local companies in your own time please share what you have done with the rest of your team so it can be used towards your business development.
Autobiographies
Remember to ask members of your family some questions about your birth and early years (any memorable events that you probably can't remember) but have been told in a story so that you can add them to your autobiography when we write them in class.
Maths homework: Averages.
We will discussing averages (in terms of data) this week. Here is a reminder of the different types of averages for you to read through and then some questions to solve (in you learning logs) at the bottom of the blog.
If we take the following numbers 2, 5, 3, 8 and 2
then the average could be 4 or 2 or 3.
This is because there are three types of average – mean, mode and median.
The Mean
The mean is where numbers would balance. If we had, for example, to find the mean of the numbers, the mean would be at the balancing point.
To calculate the mean in the numbers above we do :
2 + 5 + 3 + 8 + 2 = 20 then 20 ¸ 5 = 4
The Mode
To calculate this find the number or numbers that occurs most often. Remember mode sounds like most!
To find the mode in the numbers 2, 5, 3, 8 and 2 we notice that 2 occurs twice while 3, 5 and 8 occur only once. So the mode is 2.
It is possible that you can get two modes?
The Median
The Median is the middle number when all the numbers are written out in order, smallest first.
E.g.
Suppose we want to find the median out of these numbers:
2, 8, 3, 5, 2.
Fist we put them in order, smallest first.
2, 2, 3, 5, 8.
Which number is in the middle?
2, 2, 3, 5, 8.
The middle number is 3, so the median is 3.
What if there is no middle number??
Sometimes there will not be a middle number!
E.G
Find the median of these numbers:
1, 8, 5, 2, 9, 4
Put them in order…
1, 2, 4, 5, 8, 9
Can you see there is no one middle number?
1, 2, 4, 5, 8, 9
There are TWO middle numbers!
The median is HALF WAY between these 2 numbers.
Q. What is hal way between 4 and 5?
A. 4.5 (you can also add them together 4+5=9 and divide by 2 - this will also give you the median)
So the median will be 4.5.
Or if you had 2 of the same numbers in the middle eg. 4,3,6,4,7,1 - put them in order 1,3,4,4,6,7 there are two 4s in the middle so the median must be 4 (4+4 = 8 and divide by 2 = 4)
The Range
This is not a type of average, but it is used a lot when working out averages.
To work it out do the following sum:
BIGGEST NUMBER – SMALLEST NUMBER
E.G
Find the range of these numbers
14, 7, 23, 8, 21, 15, 13, 23.
The biggest number in the list is 23.
The smallest number is 7.
So the range is found by doing the following sum:
23 - 7 = 16
So the range is 16.
Exercise 1 (complete the following in your book - leave space to do workings and write mean, mode, median and range each time you calculate it)
1. Calculate the mean, mode, median and range of :
(a) 1, 6, 9, 5, 11, 8, 5, 13, 5.
(b) 23, 11, 17, 12, 14, 29, 30, 11, 29, 19.
(c.) 8, 3, 6, 5, 2, 10, 1, 7, 4, 9.
(d) 103, 134, 109, 112, 121, 148, 134.
(e) 9, 1, 7, 3, 5, 4, 3, 5, 4, 8, 2, 9.
2. This list shows the amounts spent by seven families on their holidays :
£100, £400, £320, £300, £5430, £100, £350.
(a) Calculate the mean, mode, median and range of these amounts.
(b) Suggest which of the three averages is the most useful indicator of how much a typical family spends on their holiday. Can you think why?
7, 8, 8, 8, 8, 9, 9, 10, 10, 11, 11,
(a) Calculate the mean, mode, and median of the data.
(b) Which of the three averages is most useful to the manager?
4. The temperature at noon on five days in January were :
|
Day
|
Monday
|
Tuesday
|
Wednesday
|
Thursday
|
Friday
|
|
Temperature (O C)
|
6
|
6
|
3
|
2
|
3
|
Calculate the mean noon temperature and the range of temperatures.
We will review the answers to these questions next Wednesday (20/01/2016) - please see
me before then if you need advice.
