Question

Construct a frequency distribution for the given data set using 6 classes. In the table, include the midpoints, relative frequencies, and cumulative frequencies. Which dass has the greatest frequency and which has the least frequency? 

Amount (in dollars) spent on books for a semester 

414 449 495 435 333 511 262 463 264 78 217 322 240369 2880 474 382 163 40479 340 70 259 241 75 176 331 279 54 

Complete the table, starting with the lowest dass limit. Use the minimum data entry as the lower limit of the first dass 

(Type Integers or decimals. Round the class limits to the nearest whole number Round all other values to the nearest thousandth as needed) 

Construct a frequency distribution and a relative frequency histogram for the accompanying data set using five classes. Which class has the greatest relative frequency and which has the least relative frequency? 

Click the icon to view the data set 

Complete the table below. Use the minimum data entry as the lower limit of the first class.

Answer 1

Solving the question 2.1.30

We first sort the data in ascending order              
Minimum value = 40              
Maximum value = 511              
Number of classes = 6              
Group width as (511-40)/6 = 78.5 = 80 (approx)              
Hence, we set group width to 80              
For each group we find the frequency of observations in that class              
Relative Frequency = Frequency/Total Observations              
Cumulative Frequency = Sum of Relative Frequency from the first class till the current class              

Frequency table is

Class	Frequency	Midpoint	Relative Frequency	Cumulative Frequency
40-119	5	79.5	0.172	5
120-199	2	159.5	0.069	7
200-279	7	239.5	0.241	14
280-359	5	319.5	0.172	19
360-439	4	399.5	0.138	23
440-519	6	479.5	0.207	29
Total	29		1

The class 200-279 has the greatest frequency = 7

The class 120-199 has the greatest frequency = 2