Question

1. communicate and justify jane interpreted the mean of the given data set, 8.48, as meaning half the cats weighed less than 8.48 pounds and half weighed more. what was janes error? explain.

weights of cats at an animal shelter (lb)

use the stem - and - leaf plot to answer 11 and 12.

1. analyze and persevere what does the mean describe in the data set?

costs of craft kits for teens ($)
1|2 3 5
2|0 2 4 5 5 7 8 8 9 5
3|0 0 2 5 5 7 8
key 1|2 - 12

1. analyze and persevere what does the range describe in the data set?
2. interpret the iqr and median in the context of the data set.

lengths of garter snakes (in.)

Explanation:

For Question 10:

Jane confused the mean with the median. The median is the value that splits a data set so half the data is below it and half is above it. The mean is the average of all values, which does not guarantee an even split of the data points above and below it, especially with skewed data like the cat weights (the data is right-skewed, with a few heavy cats pulling the mean up).

For Question 11:

The mean of the craft kit cost data set describes the average cost of a teen craft kit. It represents the typical cost if you were to distribute the total cost of all kits evenly across every kit.

For Question 12:

The range of the craft kit cost data set describes the difference between the most expensive and the cheapest teen craft kit. It measures the total spread of all cost values in the data set.

For Question 13:

• Median: The median (the line inside the box of the box plot) represents the typical length of a garter snake; half the snakes are shorter than this length, and half are longer.
• IQR (Interquartile Range): The IQR (the length of the box) represents the spread of the middle 50% of garter snake lengths. It shows the range where the most common snake lengths fall, ignoring extreme high or low values.

Answer:

1. Jane confused the mean with the median. The mean is the average, not the value that splits the data into two equal halves (that is the median).
2. The mean describes the average cost of a teen craft kit.
3. The range describes the total spread between the cheapest and most expensive craft kit.
4. - Median: Half the garter snakes are shorter than this length, half are longer; it is the typical snake length.

• IQR: It is the spread of the middle 50% of snake lengths, showing where most lengths fall.