Question

1. the following distribution lists ages of students in a college business class. class limits frequency 20 - 26 7 27 - 33 12 34 - 40 9 41 - 47 4 48 - 54 2 55 - 61 1 what is the mean? a. 18 b. 27 c. 17 d. 30

Explanation:

Step1: Find mid - points of each class

For class $20 - 26$, mid - point $x_1=\frac{20 + 26}{2}=23$.
For class $27 - 33$, mid - point $x_2=\frac{27+33}{2}=30$.
For class $34 - 40$, mid - point $x_3=\frac{34 + 40}{2}=37$.
For class $41 - 47$, mid - point $x_4=\frac{41+47}{2}=44$.
For class $48 - 54$, mid - point $x_5=\frac{48 + 54}{2}=51$.
For class $55 - 61$, mid - point $x_6=\frac{55+61}{2}=58$.

Step2: Calculate the product of mid - points and frequencies

$f_1x_1=7\times23 = 161$, $f_2x_2=12\times30=360$, $f_3x_3=9\times37 = 333$, $f_4x_4=4\times44 = 176$, $f_5x_5=2\times51=102$, $f_6x_6=1\times58 = 58$.

Step3: Calculate the sum of frequencies

$n=f_1 + f_2+f_3+f_4+f_5+f_6=7 + 12+9+4+2+1=35$.

Step4: Calculate the sum of products

$\sum_{i = 1}^{6}f_ix_i=161+360+333+176+102+58=1190$.

Step5: Calculate the mean

$\bar{x}=\frac{\sum_{i = 1}^{n}f_ix_i}{n}=\frac{1190}{35}=34$.

Answer:

34