1. Bell Work – Measures of Variability
Thursday, March 27, 2014

2. The following box plot shows the weight of different cats.
Lower (first) quartile
Median
Upper (third) quartile
Upper (maximum)extreme value
Lower (minimum)extreme value
IQR = 13 – 8 = 5
MAD cannot be found because the entire data set is not seen in a box plot.
Copy the box plot. Then, identify the following:
lower (minimum) extreme value = 6
upper (maximum) extreme value = 22
median (2nd quartile) = 11
lower (1st) quartile = interquartile range (IQR) = 5
upper (3rd) quartile = mean absolute deviation (MAD) = N/A

3. The following box plot shows the weight of different cats.
16. Analyze the variability (describe the relationships between the quartiles). Is there more variability in the lower or upper half of the data?

4. The following box plot shows the weight of different cats.
16. Analyze the variability (describe the relationships between the quartiles). Is there more variability in the lower or upper half of the data?
When comparing the first and third quartile, the range from the median is close. The range from the median to the first quartile is 11-8 = 3. The range from the median to the third quartile is 13 – 11 = 2. This means the difference between the data in these sections are about the same. Greater variability can be seen in the upper half of the data from the third quartile to the upper extreme, = 9. The range of data from the lower quartile to the lower extreme shows less variation, 8-6 = 2. The data in the lower half are grouped more closely together. The data in the upper half are more spread out.

5. The following box plot shows the test scores of 15 students.
17. Copy the box plot and describe the spread of the data.

6. The following box plot shows the test scores of 15 students.
17. Copy the box plot and describe the spread of the data.
The box plot shows that the score are very evenly
distributed. The interquartile range (middle half of the
scores) is 10. Both the bottom and top quarter of the scores
also have a range of 10 from 75 to 85 and 85 to 95,
respectively. In other words, both the minimum and
maximum values are 10 points from the median.

7. Place the following sets of numbers in order from least to greatest.
, 38% , , , , , , 0.1%
8 , , -8 , 9 , 7 , -7 , 0 , 3 , -3
, 0 , , , , 1

8. Place the following sets of numbers in order from least to greatest.
, 38% , , , , , , 0.1%
8 , , -8 , 9 , 7 , -7 , 0 , 3 , -3
, 0 , , , , 1
0.1% , 𝟎.𝟎𝟏 , 𝟏 𝟏𝟎 , 𝟑 𝟖 , 38% , 𝟑 𝟒 , 𝟎.𝟕𝟔 , 𝟓 𝟒
0.𝟎𝟎𝟏 𝟎.𝟎𝟏 𝟎.𝟏 𝟎.𝟑𝟕𝟓 𝟎. 𝟕𝟓 𝟎.𝟕𝟔 𝟏.𝟐𝟓
Renaming these rationals as decimals allows you to compare them based on their place values. Start from the left. The only number with a value in the ones place is the fraction 5/4. Therefore, 5/4 is the greatest number. Because the rest of the numbers have a 0 in the ones place, they are all less than one. From there, look at the digit in the tenths place. The lowest number is 0 and there are two numbers with a 0 in the tenths place, 0.01 and Now, you must look to the hundredths place. Because has a 0 in the hundredths place and 0.01 has a 1 in the hundredths place, we conclude that is less than The next lowest value in the tenths place is 1, so the 3rd lowest number is 0.1 or 1/10. You can also rename the rationals as percents or fractions with like denominators to compare them.
-9 , -8 , -7 , -3 , 0 , 3 , 7 , 8 , 9
- 1 , , , 0 , , 1