Question

four distributions, labeled (a), (b), (c), and (d) are represented below by their histograms. each distribution is made of 9 measurements. without performing any calculations, order their respective means $mu_{a}$, $mu_{b}$, $mu_{c}$, and $mu_{d}$. enter the four subscripts appropriately below.

Explanation:

Step1: Analyze the position of data in each histogram

The mean of a distribution can be roughly estimated by looking at the "center of mass" of the histogram. Distributions with more data on the left - hand side of the number line will have a smaller mean compared to those with more data on the right - hand side.

• Distribution (c) has most of its data concentrated on the left - hand side (around values 2 - 4).
• Distribution (a) has a bit more data towards the right compared to (c) but still less than (b) and (d).
• Distribution (b) has a relatively more balanced spread but with some data on the higher end (around 11 - 12).
• Distribution (d) has the most data on the higher end (when compared to the others) as it has a bar on the far - left (value 1) but more data towards the right (around 11 - 12) relative to (a) and (c).

Answer:

\(\mu_{c}<\mu_{a}<\mu_{b}<\mu_{d}\)