Question

graph the data
use the completed tally table to create a histogram (touching bar graph). each range will represent one bar on the graph. include a title of the graph and labels for your x and y - axis.
data analysis questions

1. what is the minimum, maximum, and range of hand span measurements in the class?
2. what is the mean (average) hand span, and how many students fall above and below this value?
3. do most hand span measurements cluster around a particular value, or are they widely spread out?
4. are there any outliers in the data? if so, how do you interpret this data?
5. why is hand span considered a trait that can show variation within a population?
6. how might genetic factors contribute to differences in hand span among students?

Explanation:

Question 1

Step1: Identify Minimum

The smallest category is "Small", so minimum hand span category is Small.

Step2: Identify Maximum

The largest category is "Large", so maximum hand span category is Large.

Step3: Calculate Range

Range is max - min (in terms of categories, from Small to Large).

Step1: Total Students

Sum the counts: \( 2 + 8 + 4 + 5 + 4 = 23 \)

Step2: Sum of Hand Span (using midpoints, assume Small = 16, 17 - 17.9 midpoint = 17.45, 18 - 18.9 = 18.45, 19 - 19.9 = 19.45, 20 - 20.9 = 20.45)

\( (16\times2)+(17.45\times8)+(18.45\times4)+(19.45\times5)+(20.45\times4) \)
\( = 32 + 139.6 + 73.8 + 97.25 + 81.8 \)
\( = 32 + 139.6 = 171.6; 171.6 + 73.8 = 245.4; 245.4 + 97.25 = 342.65; 342.65 + 81.8 = 424.45 \)

Step3: Mean

Mean \( = \frac{424.45}{23} \approx 18.45 \)

Step4: Students Above and Below

Count students with hand span > 18.45: 5 + 4 = 9; students with hand span < 18.45: 2 + 8 + 4 = 14 (adjust based on exact midpoints, but using counts: above mean (18.45) are 19 - 19.9 (5) and 20 - 20.9 (4), below are Small (2), 17 - 17.9 (8), 18 - 18.9 (4)).

Looking at the histogram counts (2, 8, 4, 5, 4), the count 8 is the highest, so most measurements cluster around the 17 - 17.9 range (the category with count 8).

Answer:

Minimum: Small, Maximum: Large, Range: From Small to Large (categories)

Question 2

First, we need to find the total number of students and the sum of hand span values (assuming the counts are 2, 8, 4, 5, 4 for categories Small, 17 - 17.9, 18 - 18.9, 19 - 19.9, 20 - 20.9).