Question

Data: 1.3, 1.4, 2.0, 2.0, 3.7, 5.0, 5.6, 6.1, 6.2, 6.4, 6.5, 6.6, 7.8

mean; 4.661538

Median; 5.6

What does the mean say about this data?

what does the median say about this data?

Propose a way/ways to give a numerical summary for this distribution. Compute these summaries. explain. I dont really understand what this question is asking?

Answer 1

We use Excel to solve this question

The summary of the data is as above
Mean = 4.661538 which indicate that distribution of the data is centerd around the mean
Median = 5.6 which indicate that middle most observation is 5.6.
Mode = 2 which indicate that most frequent observation is 2
From this summaries we have to identify distribution of the data i.e. symmetric, right tailed or left tailed.
We know that,
if mean = median = mode then distribution is symmetric.
if mean < median < mode then distribution is left tailed.
if mode > median > mean then distribution is right tailed.
Now, Observe that,

Mean < median

therefore distribution is left tailed.
Also from bar chart we see that tail part of the distribution is on left side therefore distribution is left tailed.