Question

comparing statistics visually
plot 1
plot 2
use visual clues to decide which plot has the highest measure. no calculations should be necessary, although you may use them to verify your answers.
highest mean:
highest median:
highest range:
highest interquartile ranges:

Explanation:

Highest mean:

Step1: Visual analysis of data distribution

In Plot 1, the data points (x - marks) are more concentrated towards the higher - end values (6,7,8). In Plot 2, the data is more spread out with some points at lower values (1,2). Since the mean is influenced by the values of the data points, Plot 1 has a higher mean.

Highest median:

Step1: Visual determination of middle - value position

For Plot 1, when we order the data (assuming we count the number of x - marks and find the middle one), the middle - value (median) is likely to be at a higher value (around 7). For Plot 2, the data is more spread out and lower - value data is present, so its median is lower. So Plot 1 has a higher median.

Highest range:

Step1: Visual assessment of spread from min to max

The range is \(max - min\). In Plot 1, the minimum value is 5 (assuming the left - most x is at 5) and the maximum is 8. So the range is \(8 - 5=3\). In Plot 2, the minimum is 1 and the maximum is 8. So the range is \(8 - 1 = 7\). So Plot 2 has a higher range.

Highest inter - quartile range:

Step1: Visual assessment of the spread of the middle 50%

The inter - quartile range (IQR) is \(Q3 - Q1\). In Plot 1, the data is more clustered. In Plot 2, the data is more spread out. The spread of the middle 50% (IQR) is larger in Plot 2. For example, if we consider the box - and - whisker concept (even though it's a dot - plot, we can think of quartiles), in Plot 2, there is more separation between the first and third quartiles compared to Plot 1.

Answer:

Highest mean: Plot 1
Highest median: Plot 1
Highest range: Plot 2
Highest inter - quartile ranges: Plot 2