Video Transcript
Find the median of the set of data
represented in this line plot.
The number line here goes from two
to 14. And the number of crosses
represents how many of each value we have. There are four crosses above the
number four. Therefore, we have four fours. There are six crosses above the
number five, so we have six fives. We have two sixes and two
sevens. Continuing this, we have six
eights, three nines, two 10s, three 11s, three 12s, six 13s, and three 14s. We know that the median is the
middle value when the numbers are in ascending order.
One way to answer this question
would be to write all the numbers out from smallest to largest. We would write the number four four
times. We would write the number five six
times. There would be two sixes and two
sevens. The list would continue as shown
all the way up to three 14s. There are a total here of 40
values. We could find the middle number by
crossing off one from each end, firstly, the highest number and the lowest
number. We repeat this by crossing another
four and another 14. Crossing off the next 10 smallest
numbers and next 10 largest numbers would leave us with the numbers from seven to
11. We could continue this process
until we’re left with two middle values, eight and nine.
When there are an even number of
values in total, there will always be two middle values. We can then find the median by
finding the number that is halfway between them. We do this in this case by adding
eight and nine and then dividing the answer by two. Eight plus nine is equal to 17, and
half of this is 8.5. Clearly, 8.5 is halfway between
eight and nine. Therefore, this is the median of
the set of data.
An alternative method here would be
to calculate the median position first. The median position can be
calculated using the formula 𝑛 plus one divided by two, where 𝑛 is the total
number of values. 40 plus one is equal to 41. And dividing this by two gives us
20.5. As 20.5 lies between the integers
20 and 21, we know that the median will be halfway between the 20th and 21st
value.
To find the 20th and 21st values,
we can work out the running total or cumulative frequency. We do this by adding the number of
values we have. Four plus six is equal to 10. Adding another two gives us 12. This means that 12 values are six
or lower. Adding another two gives us 14, and
adding six gives us 20. This means that there are 20 values
that are eight or less. As there are 40 values in total,
there must therefore be 20 values that are nine or greater. The 20th value is equal to eight,
and the 21st value is equal to nine. Once again, finding the midpoint of
these two values gives us a median of 8.5. This method is useful when we have
a large number of values as it saves writing out the whole data set.
