10.1 calculating statistics.
you can use statistics to summarise sets of data. you can also use them them to compare different sets of data. you should already be able to calculate three different averages: the median and the mean.remember that the range is not an average. it measures how spread out of set of value or number is.
for a large set of data is not practical to list every number separately. instead, you can record the data in frequency data.
The mode is the most common value or number.
The median is the middle value, when they are listed in
order.
The mean is the sum of all values divide by the number of
value.
The range is the largest value minus the smallest.
A frequency is any table that records how often (frequently data
occur.
example:
the table shows the number of beads on 200 necklaces
Number of beads
|
25
|
30
|
35
|
40
|
45
|
50
|
frequency
|
34
|
48
|
61
|
30
|
15
|
12
|
a. the mode is 35 à the mode is the number with the highest frequency
b. 6900÷200= 34.5 à
(25 x 34 x 48 + 35 x 61 + 40 x 30 + 45 x 15 + 50 x 12 )÷ the sum of all the frequencies. This is a reasonable
answer because its near the middle of all the possible number of beads.
c. 50-25=25 this is the difference between the largest and smallest number of beads.
10.2 using statistics
now you can work out several different statistical measures. in a real situation, you need to decide which one to use. if you want to measure how spread out of a set of measurement is, the range is the most useful statistics. if you want to find a representative measurement, you need an average. should it be the mode, the median or mean? that depends on the particular situation. here is the summary to help you decide which average to choose.
- choose the mode if you want to know which is the most commonly occurring number.
- the median is the middle value, when the data values are put in order.half the numbers are greater than the median and half the numbers are less than the median.
- the mean depends on every value. if you change one number you change the mean
example:
here are the ages, in years, of the players in a football team. work out the average age.give a reason for your choice of averages.
16,17,18,18,19,20,20,21,21,32,41.
the mode is not a good choice. --> there are three modes. each has a frequency of only two
the mean will be affected by two oldest people. --> they are much older and will distort the value. in the fact the mean is 22.1 and nine people are younger than this; only two are older.
the median is 20 and this is the best average to use in this case. --> five players are younger than the median and five are older.
16,17,18,18,19,20,20,21,21,32,41.
the mode is not a good choice. --> there are three modes. each has a frequency of only two
the mean will be affected by two oldest people. --> they are much older and will distort the value. in the fact the mean is 22.1 and nine people are younger than this; only two are older.
the median is 20 and this is the best average to use in this case. --> five players are younger than the median and five are older.
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