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This section
explored the many different problems you may be faced with when having to
find an average. It also shows
a number of examples of COMPARING distributions. |
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AVERAGES from Tables Below is an
example of a table of CONTINUOUS data To estimate the mean: · We to find the mid-points of each of the classes which I will write in red · We also need to find the total
frequency
To estimate the MEDIAN without drawing a cumulative
frequency graph To find
which value is the MEDIAN we use the formula In this
case, n=12 The 6^{th}
and the 7^{th} value are both in the class: . So our median class
is |
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AVERAGES from STEM and LEAF diagrams This
table shows pocket money of boys in a
class
We already know that the girls have got a mean of £23, a
median of £26 and a range of £30. QUESTION: Compare the amount which boys and girls
receive in pocket money. Boy’s
mean: we
need to add up each value in the stem and leaf diagram and divide by the
number of numbers there are Boy’s
median: we
know that n=21 If we count along to
find the 11^{th} value we find it is £25 Boy’s
range:
Comparison: 1)
The
boys’ range is £42 which is £12 more than the girl’s range. This means the
amount which boy’s received is more spread out/less consistent. 2)
The
boy’s mean of £29.50 is £6.50 more than the girl’s mean. However, the boy’s
median of £25 is £1 less. On balance, however, you would suggest that the higher
mean indicated that boy’s, on average, receive MORE pocket money |
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MEDIAN’s and QUARTILES WITHOUT a cumulative
frequency graph Assuming the data is given in ascending
order (if not, you need to re-arrange it first) KEY FORMULA:
(where n=the number of data values) Example:
(numbers is red link to the LQ and UQ below) |