Question

female shoe sizes
graph: create a histogram of the female shoe sizes (each size is one bin).
5 6 6 6 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8
8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9
9 9 9 10 10 10 10 10 10 10 10 10 11 11 11 11 11 12 12
mean ($\bar{x}$) = 8.63 median = 9 mode =
q: what do you notice about all of these numbers?
shape = symmetric standard deviation ($s_x$) = 518

Explanation:

Step1: Count frequency of each size

Count how many times each shoe - size appears in the data set. For example, size 5 appears 1 time, size 6 appears 3 times, etc.

Step2: Determine mode

The mode is the number that appears most frequently in a data - set. Counting the frequencies: size 7 appears 10 times, size 8 appears 10 times, size 9 appears 13 times, size 10 appears 7 times, size 11 appears 5 times, size 12 appears 2 times. So the mode is 9 (since 9 appears the most number of times).

Step3: Analyze the numbers

The mean is 8.63, the median is 9, and the mode is 9. The shape is symmetric. The mean, median and mode are relatively close in value. This is characteristic of a symmetric distribution. When a distribution is symmetric, the mean, median and mode tend to be approximately equal.

Answer:

Mode = 9
Observation: The mean (8.63), median (9) and mode (9) are relatively close, which is typical for a symmetric distribution.