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 36 0.12 61 42 - 52 68

Explanation:

Step1: Calculate mid - point

The mid - point of a class interval $a - b$ is $\frac{a + b}{2}$. For the class $42-52$, the mid - point is $\frac{42+52}{2}=\frac{94}{2}=47$.

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 $\frac{f}{n}$, where $f$ is the frequency of the class. For the class $42 - 52$ with $f = 68$, the relative frequency is $\frac{68}{365}\approx0.19$.

Step4: Calculate cumulative frequency

The cumulative frequency of a class is the sum of the frequencies of that class and all previous classes. For the class $42 - 52$, the cumulative frequency is $17+44 + 68=129$.

Answer:

Class	Frequency, f	Midpoint	Relative frequency	Cumulative frequency
31 - 41	44	36	0.12	61
42 - 52	68	47	0.19	129