Video Transcript
A weather station has four
barometers that measure the air pressure. Their results are in the table
below. Air pressure is measured in a unit
called pascals. If the true air pressure is known
to be exactly 101,000 pascals, which of the four barometers produces the most
accurate set of results?
A barometer is a device that can
measure air pressure. In this question, we are given four
sets of data, each one measured by a different barometer. Each barometer measures six values
for the air pressure. Here, we’ve been asked to decide
which barometer has produced the most accurate set of results. Let’s start by reminding ourselves
of what accurate means.
The accuracy of a measurement
indicates how close the measured value is to the true value of the quantity. If the measured value is very close
to the true value, then that measurement is very accurate. But if the measured value is
nowhere near the true value, then that measurement is not very accurate.
So to answer this question, we need
to work out which barometer measures an air pressure that is closest to the true
value, which we’re told is 101,000 pascals. But we’re not just looking at
single measurements, we have to assess the overall accuracy of the whole set of data
produced by each barometer.
For example, let’s take a look at
the measurements made by barometer one. The first two measurements made by
barometer one are exactly equal to the true value of the air pressure, 101,000
pascals. So these two measurements on their
own are very accurate. But if we look at the rest of the
measurements made by barometer one, we see that these are all much higher than the
true value. So when we consider the whole set
of all six measurements made by this barometer, overall, this set of data is not
particularly accurate.
We can express this idea
mathematically by calculating the average value of the measurements made by this
barometer. To assess the overall accuracy of
the whole set of data, we can compare the average value measured by the barometer to
the true value of the air pressure. Clearing some space at the bottom
of our screen, to find the average value, we add up all the individual measurements
and then divide the total by the number of measurements in the data set, which is
six.
Reading the data from the first row
of the table, the average value measured by barometer one is equal to 101,000
pascals plus 101,000 pascals plus 135,000 pascals plus 112,000 pascals plus 125,000
pascals plus 130,500 pascals all divided by six. This gives us an answer of
approximately 117,400 pascals. This is pretty far away from the
true value of the air pressure, which is 101,000 pascals. So just like we said before, this
set of data isn’t very accurate.
So now we’ve seen how we can assess
the accuracy of a set of data by comparing the average value of the measurements to
the true value of the quantity. In this question, we have been
asked to determine which barometer is the most accurate. To do this, we simply need to
calculate the average value measured by each barometer and see which is closest to
the true value of the air pressure.
Next, let’s calculate the average
of the values measured by barometer two. All the measurements made by
barometer two have the same value, 110,000 pascals. From this, we might be able to tell
straightaway that the average of these values is also 110,000 pascals. But we can still calculate the
average by summing up these six values and dividing by six. This gets us an average value of
110,000 pascals.
Next, Let’s look at barometer
three. Looking at this data set, we can
see that all of these values are actually very close to the true value of the air
pressure, 101,000 pascals. So this data set seems to be very
accurate. Because of this, we would expect
the average value of the measurements to be very close to the true value of the air
pressure. If we calculate the average, we
find that this value is equal to 100,000 pascals plus 102,000 pascals plus 101,500
pascals plus 100,000 pascals plus 101,000 pascals plus 100,000 pascals all divided
by six. This gives us an average value of
100,750 pascals.
Finally, let’s look at barometer
four. The average of these values is
101,000 pascals plus 151,000 pascals plus 80,000 pascals plus 141,000 pascals plus
121,000 pascals plus 89,000 pascals all divided by six. This gives us an average value of
113,000 pascals.
Now that we have calculated the
average value measured by each barometer, we can compare them all to the true value
and decide which barometer has given the most accurate set of results. To make these values easier to
compare, we can write them in a table like this. Remember that the true value of the
air pressure is equal to 101,000 pascals. We can see that the average value
measured by barometer three is closest to the true value of the air pressure. So barometer three must be the
barometer that produces the most accurate set of results. Hence, the correct answer is
barometer three.
