Statistic can be use to summarise sets of data, and also use them to compare sets of data.
There are three different average:
- Mode: most common value or numaber
- Median: the middle value, when they listed in order
- Mean: the sum of all the value divided by the numbers of values.
Range is not an average. it measure how spread out a set of values or numbers is.
For a large set of data, its not practical to list every number separately. instead you can record the data in frequency table.
EXAMPLE:
the table shows the number of breads on 200 necklaces
Number of breads: 25, 30, 35, 40, 45, 50
Frequency : 34, 48, 61, 30, 15, 12
A. find the mode
B. Find the mean
C. Find the range
ANSWER:
A. The mode is 35
B. (25x34 + 30x48 + 35x61 + 40x30 + 45x15 + 50x12) = 6900
6900 divided by 200(sum of all frequencies) = 34.5
C. 50 - 25 = 25 (this is the difference between the largest and the smallest number of bread)
USING STATISTIC: 10.2
If you want to measure how spread out a set of measurement is, the range is the most useful statistic.
Here is a 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 put in order. half the numbers are greater than the median and the half the number are less than the median
- the mean depends on every value. if you change one number you can change the mean.
EXAMPLE:
Here are the ages, in years, of the football players in football team.
Work out the average age.
16, 17, 18, 18, 20, 20, 21, 21, 32, 41
- The mode is not good choice. There are three modes. Each has a frequency of only 2.
- The mean will be affected by two oldest people. they are much older and will distort the value. In 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 player are younger than the median and five are older
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