Question

1. which hair color occurs most often?
2. from the information in the data table, can you find the number of boys with black hair? why or why not?
3. what information can you give about the number of students with black hair?
4. which class has the most blond students?
5. how many students make up the entire student population?

exercise 2: averages
place information from class in the following data table:
data table 2: student height *note = feet; \ = inches

height	number of females	number of males
below 5 (60 in)	0	0
5 - 52\ (62 in)	6	1
53\ - 54\ (64 in)	1	1
55\ - 57\ (67 in)	4	2
58\ - 510\ (70 in)	2	1
511\ - 61\ (73 in)	0	3
above 61\ (75 in)	0	3

answer the following questions based on the data table above.

1. how many students make up the same group?
2. what is the average height of all students in this class using inches?
3. what is the average height of the males in class? females?
4. on average, are males taller or females?
5. how could you improve the results?

Explanation:

Step1: Calculate total number of students in each height - group

For each row in the table, add the number of females and males.
For example, for the height range \(5' - 5'2''(62\text{ in})\), the number of students is \(6 + 1=7\).

Step2: Calculate total number of students in all groups

Sum up the number of students in each height - group.
\[

$$\begin{align*} &(0 + 0)+(6 + 1)+(1+1)+(4 + 2)+(2 + 1)+(0+3)+(0 + 3)\\ =&0+7 + 2+6+3+3+3\\ =&24 \end{align*}$$

\]

Step3: Calculate total height of all students

Multiply the mid - point of each height range by the number of students in that range, then sum these products.
For \(5' - 5'2''(62\text{ in})\): \(62\times(6 + 1)=434\)
For \(5'3'' - 5'4''(64\text{ in})\): \(64\times(1 + 1)=128\)
For \(5'5'' - 5'7''(67\text{ in})\): \(67\times(4 + 2)=402\)
For \(5'8'' - 5'10''(70\text{ in})\): \(70\times(2 + 1)=210\)
For \(5'11'' - 6'1''(73\text{ in})\): \(73\times(0 + 3)=219\)
For \(Above\ 6'1''(75\text{ in})\): \(75\times(0 + 3)=225\)
The sum of these products is \(434+128 + 402+210+219+225 = 1618\)
The average height of all students is \(\frac{1618}{24}\approx67.42\) inches

Step4: Calculate total height and number of male students

Sum the number of male students: \(0 + 1+1+2+1+3+3=11\)
Calculate the total height of male students:
For \(5' - 5'2''(62\text{ in})\): \(62\times1 = 62\)
For \(5'3'' - 5'4''(64\text{ in})\): \(64\times1=64\)
For \(5'5'' - 5'7''(67\text{ in})\): \(67\times2 = 134\)
For \(5'8'' - 5'10''(70\text{ in})\): \(70\times1=70\)
For \(5'11'' - 6'1''(73\text{ in})\): \(73\times3=219\)
For \(Above\ 6'1''(75\text{ in})\): \(75\times3=225\)
The sum of these products is \(62+64+134+70+219+225 = 774\)
The average height of male students is \(\frac{774}{11}\approx70.36\) inches

Step5: Calculate total height and number of female students

Sum the number of female students: \(0+6 + 1+4+2+0+0 = 13\)
Calculate the total height of female students:
For \(5' - 5'2''(62\text{ in})\): \(62\times6=372\)
For \(5'3'' - 5'4''(64\text{ in})\): \(64\times1 = 64\)
For \(5'5'' - 5'7''(67\text{ in})\): \(67\times4=268\)
For \(5'8'' - 5'10''(70\text{ in})\): \(70\times2=140\)
The sum of these products is \(372+64+268+140 = 844\)
The average height of female students is \(\frac{844}{13}\approx64.92\) inches

Answer:

1. \(24\)
2. Approximately \(67.42\) inches
3. Approximately \(70.36\) inches; Approximately \(64.92\) inches
4. Males
5. Increase the sample size (collect data from more students)