Question

bridge 1: suspicious descriptions
for each picture and description (a - e), state whether you agree or disagree, and explain your reasoning.
given the shape of the distribution, determine whether youd use mean or median as a measure of center.
claims
agree/
disagree
explain your reasoning
use the shape of the
distribution to determine the
best measure of center to
use.
a. the data is bell - shaped since
there is a central peak for
symmetric data values that
are less frequent on the ends.
therefore, i would recommend
using ______________ as
the measure of center.
b. the data is symmetric
because if the distribution
was cut in half, both sides
would be the same shape.
therefore, i would recommend
using ______________ as
the measure of center.
c. the data is uniform because
there seems to be the same
amount of data points across
the entire distribution.
therefore, i would recommend
using ______________ as
the measure of center.

Explanation:

• For claim a:
• A bell - shaped distribution is symmetric and has a single central peak. The given histogram has a central peak and is symmetric (the left and right sides are mirror images). So, we agree with the claim.
• For a symmetric (bell - shaped) distribution, the mean is the best measure of center because in a symmetric distribution, the mean, median, and mode are all equal, and the mean takes into account all the data values.
• For claim b:
• The dot - plot is symmetric. If we fold the dot - plot along the vertical line passing through the center (around \(x = 2\)), the two sides will match. So, we agree with the claim.
• In a symmetric distribution (like the dot - plot here), the mean is the best measure of center as it balances the data values on either side of the center.
• For claim c:
• A uniform distribution has approximately the same number of data points in each interval. The given histogram has an increasing number of data points as \(x\) increases. So, we disagree with the claim.
• Since the distribution is skewed (right - skewed in this case, as the tail is on the right side), the median is a better measure of center. The mean is pulled towards the tail (higher values) in a skewed distribution, while the median is less affected by extreme values.

Answer:

• a. Agree. The histogram is symmetric with a central peak. Mean
• b. Agree. The dot - plot is symmetric. Mean
• c. Disagree. The histogram is not uniform (it is increasing). Median