Video Transcript
Mason took a sample of 100
balls from a box. He weighed each ball and
recorded its weight in the table. He used the data to draw the
cumulative frequency graph shown on the grid. Estimate how many balls had a
weight of less than 80 grams. Estimate how many balls had a
weight of 130 grams or more.
Cumulative frequency is the sum
of all the previous frequencies up to the current point. It is often referred to as the
running total of frequencies. The given graph shows the
cumulative frequency of the weights of 100 balls. We can see from the graph that
the highest cumulative frequency is 100. Any point on the cumulative
frequency graph indicates the total number of balls that are less than the given
weight.
In order to find an estimate
for the number of balls that are less than 80 grams, we can draw a vertical line
from 80 on the đť‘Ą-axis until it meets the curve. We then draw a horizontal line
from this point to the 𝑦-axis to allow us to read the corresponding 𝑦-value,
the cumulative frequency. Observing that each minor grid
line on the 𝑦-axis represents a frequency of two, we can give the answer to the
first part of this question. The number of balls less than
80 grams can be estimated as 26 balls.
Although each value on the
cumulative frequency curve represents frequencies that are less than a
particular value, we can still use the curve to find the values for greater than
or equal to values. To estimate the number of balls
that are 130 grams or more, we use the same process. We draw a vertical line from
130 on the đť‘Ą-axis to the curve and then draw a horizontal line from this point
to the 𝑦-axis. We can read the cumulative
frequency of 78 balls from the 𝑦-axis, which means that 78 balls had a weight
less than 130 grams.
In order to find the number of
balls that had a weight of 130 grams or more, we subtract this from the total
frequency. The total frequency is the
total number of balls that have been weighed. Hence, it is 100. Therefore, we have 100 minus
78, which is equal to 22. The answer to the second part
of the question is that we estimate that there are 22 balls with a weight of 130
grams or more.
