Question

it seems these days that students have to work more and more each week to be able to afford the costs of college. for a recent labor survey conducted by the government, there were 76 respondents who were working while attending college. the frequency distribution below summarizes the number of hours worked per week as reported by the respondents.

hours per week	26 to 30	31 to 35	36 to 40	41 to 45	46 to 50	51 to 55

based on the frequency distribution, using the midpoint of each data class, estimate the mean number of hours worked per week by the respondents. for your intermediate computations, use four or more decimal places, and round your answer to one decimal place.

Explanation:

Step1: Find midpoints of each class

For class 26 - 30: Midpoint $m_1=\frac{26 + 30}{2}=28$
For class 31 - 35: Midpoint $m_2=\frac{31 + 35}{2}=33$
For class 36 - 40: Midpoint $m_3=\frac{36 + 40}{2}=38$
For class 41 - 45: Midpoint $m_4=\frac{41 + 45}{2}=43$
For class 46 - 50: Midpoint $m_5=\frac{46 + 50}{2}=48$
For class 51 - 55: Midpoint $m_6=\frac{51 + 55}{2}=53$

Step2: Calculate $f_i\times m_i$ for each class

• Class 26 - 30: $f_1 = 8$, $f_1\times m_1=8\times28 = 224$
• Class 31 - 35: $f_2 = 25$, $f_2\times m_2=25\times33 = 825$
• Class 36 - 40: $f_3 = 18$, $f_3\times m_3=18\times38 = 684$
• Class 41 - 45: $f_4 = 14$, $f_4\times m_4=14\times43 = 602$
• Class 46 - 50: $f_5 = 7$, $f_5\times m_5=7\times48 = 336$
• Class 51 - 55: $f_6 = 4$, $f_6\times m_6=4\times53 = 212$

Step3: Sum of $f_i$ and sum of $f_i\times m_i$

Sum of $f_i$: $8 + 25 + 18 + 14 + 7 + 4=76$
Sum of $f_i\times m_i$: $224+825 + 684+602+336+212=2883$

Step4: Calculate the mean

Mean $\bar{x}=\frac{\sum f_i\times m_i}{\sum f_i}=\frac{2883}{76}\approx37.9$

Answer:

37.9