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

Explanation:

Step1: Calculate mid - point

The mid - point of a class interval $a - b$ is $\frac{a + b}{2}$. For the class $20 - 30$, the mid - point is $\frac{20+30}{2}=25$.

Step2: Calculate total frequency

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

Step3: Calculate relative frequency

The relative frequency of a class is $\frac{f}{n}$. For the class $20 - 30$ with $f = 17$, the relative frequency is $\frac{17}{365}\approx0.05$.

Step4: Calculate cumulative frequency

The cumulative frequency of the first class is equal to its frequency. For the class $20 - 30$, the cumulative frequency is $17$.

Answer:

Class	Frequency, f	Midpoint	Relative frequency	Cumulative frequency