Question

use the frequency distribution shown below to construct an expanded frequency distribution. high temperatures (°f)
class 20 - 30 31 - 41 42 - 52 53 - 63 64 - 74 75 - 85 86 - 96
frequency, f 17 44 68 69 76 68 23

complete the table below.
high temperatures (°f) (round to the nearest hundredth as needed.)
class frequency, f midpoint relative frequency cumulative frequency
20 - 30 17 25 0.05 17
31 - 41 44

Explanation:

Step1: Calculate the mid - point for the class 31 - 41

The mid - point formula for a class interval $a - b$ is $\frac{a + b}{2}$. For the class 31 - 41, the mid - point $x=\frac{31 + 41}{2}=\frac{72}{2}=36$.

Step2: Calculate the total frequency

The total frequency $n=17 + 44+68 + 69+76+68+23=365$.

Step3: Calculate the relative frequency for the class 31 - 41

The relative frequency formula is $\text{Relative Frequency}=\frac{\text{Frequency}}{\text{Total Frequency}}$. For the class 31 - 41 with frequency $f = 44$, the relative frequency $rf=\frac{44}{365}\approx0.12$.

Step4: Calculate the cumulative frequency for the class 31 - 41

The cumulative frequency is the sum of the frequencies of all classes up to and including the current class. For the class 31 - 41, the cumulative frequency $cf=17 + 44 = 61$.

Answer:

Class	Frequency, f	Midpoint	Relative frequency	Cumulative frequency
31 - 41	44	36	0.12	61