Question

a professor posts each of her video lectures online. the lengths of these lectures (rounded to the nearest minute) are represented in the following dot plot.\
lecture lengths (minutes)\
which statement correctly describes the data in this dot plot?\
show your work here\
\
\bigcirc median = mode \qquad \bigcirc mean > mode\
\bigcirc mode = mean \qquad \bigcirc mode > median

Explanation:

Step1: List all data points

$42, 42, 42, 43, 43, 43, 43, 44, 44, 45, 45, 45, 46, 46, 47, 48, 48, 48$

Step2: Find the mode

Mode = most frequent value = $43$

Step3: Find the median

Total data points: $n=18$. Median = average of 9th and 10th values: $\frac{44+45}{2}=44.5$

Step4: Calculate the mean

Mean = $\frac{3(42)+4(43)+2(44)+3(45)+2(46)+1(47)+3(48)}{18}$
$=\frac{126+172+88+135+92+47+144}{18}=\frac{804}{18}\approx44.67$

Step5: Compare values

Mean ($\approx44.67$) > Mode ($43$)

Answer:

mean > mode