Video Transcript
As part of a childcare course,
students recorded the age, in months, at which a group of babies and toddlers
began to walk. The data is recorded in the
grouped frequency table below. Complete the descending
cumulative frequency table.
Let’s recall that the
descending cumulative frequency of a value 𝑥 indicates that frequency of values
that are greater than or equal to 𝑥. In the grouped frequency table,
we are given groupings such as eight dash, 10 dash, along with their
frequencies. For example, the class eight
dash indicates ages that are eight months or greater but less than 10 months,
the lower boundary of the subsequent class. In the second table, the first
column relates the group aged eight months or more and a descending cumulative
frequency.
We know from the total
frequency that this study involves 150 babies and toddlers. From the table, we can observe
that two babies started walking at eight months or more up to 10 months. But the babies that started
walking at 10 dash months, 12 dash months, and so on up until 18 dash months
also started walking at eight months or more. Therefore, the first cumulative
frequency will be the total frequency of 150. All 150 babies and toddlers
recorded were walking at an age of eight months and more. Hence, our first entry in the
descending cumulative frequency row is 150.
To find the second descending
cumulative frequency for the group 10 or more, we will now exclude the two
babies from the first class who walked at an age less than 10 months. In other words, to find the
second descending cumulative frequency, we subtract the first frequency from the
previous descending cumulative frequency. This gives 150 minus two, which
equals 148.
To find the third descending
cumulative frequency of the group 12 or more, we subtract both frequencies of
the groups eight dash and 10 dash months from the total frequency. Alternatively, we can consider
this as subtracting the second frequency of 15 from the second descending
cumulative frequency of 148. This gives us 133.
To find the fourth descending
cumulative frequency, we subtract the frequency of 40 from the third descending
cumulative frequency. This gives 133 minus 40, which
is equal to 93.
We can then complete the
remaining cumulative frequency values in the same way. Notice that the last descending
cumulative frequency value is zero. In the first table, the last
class is that of 18 dash, meaning a time period of 18 months or more. We can assume that this group
has the same class width as the previous group. Hence, this group is babies or
toddlers who walked less than 20 months. Therefore, the descending
cumulative frequency value of zero for the class 20 or more is correct. There were zero toddlers
recorded as having started walking at 20 months or more.
We can give the answer that the
missing descending cumulative frequency values are 150, 148, 133, 93, 42, seven,
and zero.
