the density of people per square kilometer for 56 countries is in the table. create a frequency…

Explanation:

Step1: Determine class limits

The first lower - class limit is 28. Since the class width is 75, the class limits are: Class 1: 28 - 102 Class 2: 103 - 177 Class 3: 178 - 252 Class 4: 253 - 327 Class 5: 328 - 402 Class 6: 403 - 477 Class 7: 478 - 552 Class 8: 553 - 627

Step2: Calculate frequency

Count the number of data values that fall into each class. For example, for the class 28 - 102: The data values 44, 28, 102, 66, 36, 101, 28, 52, 37, 87, 31, 49, 33, 56, 108, 120, 117 fall into this class. So the frequency $f_1 = 17$. Repeat this process for all classes.

Step3: Calculate relative frequency

The relative frequency of a class is given by $rf_i=\frac{f_i}{n}$, where $n = 56$ (total number of data points). For example, for the first class with $f_1 = 17$, $rf_1=\frac{17}{56}\approx0.3036$. Calculate $rf_i$ for all classes.

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 first class, the cumulative frequency $cf_1=f_1 = 17$. For the second class, if $f_2$ is the frequency of the second class, then $cf_2=f_1 + f_2$. Calculate $cf_i$ for all classes.

The completed table:

Class limits	Frequency	Relative frequency	Cumulative frequency
28 - 102	17	0.3036	17
103 - 177	7	0.1250	24
178 - 252	5	0.0893	29
253 - 327	7	0.1250	36
328 - 402	7	0.1250	43
403 - 477	4	0.0714	47
478 - 552	4	0.0714	51
553 - 627	5	0.0893	56

Answer:

Class limits	Frequency	Relative frequency	Cumulative frequency
28 - 102	17	0.3036	17
103 - 177	7	0.1250	24
178 - 252	5	0.0893	29
253 - 327	7	0.1250	36
328 - 402	7	0.1250	43
403 - 477	4	0.0714	47
478 - 552	4	0.0714	51
553 - 627	5	0.0893	56