Math Made Easy: Finding the mode, mean, median, and range of a set of numbers (part 2)
http://www.voutube.com/watch?v=tgxZfQDf4qY
Listen to and watch the video and try to answer the questions.
1. What is the mean of a set of numbers?...................................................
2. Why should you be interested in a 7 day weather forecast?...........................
3. Is this forecast reliable?.....................................................................
4. How do you proceed if you want to get a mean of a set?
a) .................................................................
b) .................................................................
5. How do you round numbers?................................................................
Work with your neighbor and try to describe how you can find
1. the mode of a set....................................................'.................
2. the median of a set
3. the range of a set.
(now make similar sentences beginning with the following words :
6. Look at tliis table:
QUESTION
How high is that building?
What is the height of that buildina?
j answer
i It is 200 m high.
| The height of that building is 200 m, | OR It has a height of 200 in.
Use the table to ask and answer questions about the following:
(Note: The first pair is not always possible, and should not be used in (0and(g)).
a) hciiiht?
e) age?
3600 years
-4 cm -
b) width'.'
leneth? 1 cm
area ;
f) top speed? capacity? weight? 750 cm3
500 kg 120km hr-
či  thickness'.' «■
40 mm
Ú) depth?
e.) temperature? density?
15"C       800kg m"3
7. Look and read :
• Temperature is measured in degrees Celsius.
• The degree Celsius is a unit of temperature.
a)
b)
c)
d)
e)
The joule The newton Time Mass The watt
ľ) S)
h)
i) j)
Velocity Loudness Electric current The litre Angles
Section 3 Reading
25
Read this:
Different kinds of average
The word 'average' is used frequently; for example, we talk about 'the average mark' in a test, the 'average rainfall' for a particular geographicai location, or the 'average distance' of the Earth from the Sun' There are, however, many different kinds of average: here are some examples.
1   The arithmetical mean
1 Mon. 13
Tues, 12
Wed. rTThurs
Fri.
1 I I
Sai.
Sun.
In a certain town, the temperature is recorded at mid-day each day in a particular week. The results arc shown above. The 'average' is
13 + 12 + 5 + 8 + 4 + 5 + 9    0 .    ,, , ,,     .,     . ,
-'-=-= 8, and this is called the arithmetical mean.
2   The midrange
A maximum-minimum thermometer shows that the maximum temperature yesterday was 13°C and the minimum 2° C, i.e. the range is from 18° to 2JC. and 18° C and V C are the extremes of the range. The 'average'
!8 + 2
= 10'C   is called the mean of
the extremes or the midraniic.
A/ o t iE i)$ WT h ed fi T) a, b: hüll , i o/og miJ,
; ne rnectiaii
a tape measure
With ;i tape measure, we can find the arithmetical mean of the heights of the people shown above. Without a tape measure, we can use a different kind of average. First, we arrange the people in ascending or descending order of height. We then select the middle member of this ordered set. This kind of average is known as the median.
an ordered set (descending)
4   The mode
an ordered set (ascending)
Of the forty families who live in our street, 36 own a television set, 3 own 2 television sets, and one doesn't have a television set. If we take the arithmetical mean, we find that the 'average' family owns 1-05 television sets. A more useful average in this case is the mode i.e. the most common number, in this case one.
5   The geometric mean
1950
A man bought ten rabbits in 1950. In [970, he had 200 rabbits. How many did he have in I960? The answer is not the arithmetical mean of 10 and 200 i.e. 105, because population does not grow arithmetically
(e.g. 2, 4, 6, 8.......) but geometrically (e.g. 2. 4, 8. 16, 32, ..,...,.). The
geometric mean of 10 and 200 is N/l 0 x 200 =^ 45.
9. Solve these problems:
a) Find-the median, the mode, the arithmetical mean and the midrange of the following set of values.
11   14   16   4   9   9 14
b) Find the geometric mean of the following pairs:
3 and 27;   10 and 1000;   2 and 8192"
10. Using words from the list, complete the definitions of the different kinds of average:
central divided divided maximum
minimum
number
occurs
ordered
product
square root sum sum value
a) The arithmetical mean of a set is the___________of the members of
the set_by the,______of members.
b) The midrange of a set is the________of the............. . and
_values of a set_____by two.
c) The mode of a set is the _________ which _._ ... . most
frequently.
d) The median of a set is the___„ value of an _._   ..... set.
e) The geometric mean of two numbers is the ... of the ________of the numbers.
11. Read and answer:
The following sets of numbers are arithmetical or geometrical progressions. Decide which is which and say why.