Video Transcript
Which of the statements is correct
for the distribution represented by the diagram? (A) The distribution is
symmetric. (B) The distribution has an outlier
at six. (C) The distribution has a gap from
21 to 29. (D) The distribution has a cluster
from seven to 20. Or (E) the distribution has a peak
at 22.
To find which of these is correct,
we’ll consider them one at a time. First, the distribution is
symmetric. To find out if this distribution is
symmetric, you can sketch a line over the distribution. This image is not symmetric. The six is stretching out the
image. And so, we can’t say that the
distribution is symmetric.
Now, let’s consider statement (B)
the distribution has an outlier at six. To consider a six as an outlier, we
want to look at the spread of the data points. All of the other data points fall
between 21 and 29. The distance from 6 to 21 is
15. We can say that the data point six
is quite far removed from the rest of the data. And therefore, it is a true
statement to say that this distribution has an outlier at six. But we want to go ahead and check
the other three statements.
The distribution has a gap from 21
to 29. Since the majority of the points
fall between 21 and 29, there is no gap there. Option (D) the distribution has a
cluster from seven to 20. There are, in fact, no data points
from seven to 20, which means there can’t be a cluster there. And finally, option (E) the
distribution has a peak at 22. If we look closely at 22, there’s
only one data point there. Looking across our diagram, we see
that the peak happens at 26, which means option (E) is not correct, leaving us with
only one true statement. The distribution has an outlier at
six.
