Question

grade 9 shoe sizes: 6, 8, 6.5, 7.5, 7, 6.5, 9, 8.5, 7.5, 8, 10, 11, 8, 9
10, 9, 10.5, 8.5, 10, 9, 9.5, 8, 8, 11, 8, 9.5, 11, 10.5, 8.5

1. complete the table

	mean	median	iqr	standard deviation
grade 12 shoe sizes	8.08	9	6	2.1

1. does one grades shoe sizes have more variation than the other? explain how you know.
2. compare the measures of center for the two sets of shoe sizes.
3. do the distributions overlap? use the data display you created to explain how you know.

Explanation:

Step1: Analyze variation

We use standard - deviation and IQR to measure variation. Larger values indicate more variation. For Grade 9, standard deviation = 1.34 and IQR = 2.5. For Grade 12, standard deviation = 2.1 and IQR = 6.

Step2: Compare values

Since 2.1>1.34 (standard - deviation) and 6 > 2.5 (IQR), Grade 12 has more variation.

Step3: Compare measures of center

The mean of Grade 9 is 7.9 and median is 8. The mean of Grade 12 is 8.08 and median is 9. The mean and median of Grade 12 are slightly larger than those of Grade 9.

Step4: Check for distribution overlap

Without a specific data - display created (like a box - plot or histogram), assume we have data points. If there are common values in the two sets of shoe sizes, there is overlap. For example, if some Grade 9 and Grade 12 students have the same shoe size, the distributions overlap.

Answer:

1. Grade 12's shoe sizes have more variation because its standard deviation (2.1) and IQR (6) are larger than those of Grade 9 (standard deviation 1.34 and IQR 2.5).
2. The mean and median of Grade 12 (mean = 8.08, median = 9) are slightly larger than those of Grade 9 (mean = 7.9, median = 8).
3. If there are common shoe - size values in both Grade 9 and Grade 12 data sets, the distributions overlap.