the data represent the time, in minutes, spent reading a political blog in a day. construct a frequency…

Explanation:

Step1: Find range

The data set is (0,0,1,1,2,3,5,6,7,7,7,8,8,11,11,18,18,19). The maximum value (M = 19) and the minimum value (m=0). The range (R = M - m=19 - 0 = 19).

Step2: Determine class - width

We want 5 classes. The class - width (w=\frac{R}{n}), where (n = 5). So (w=\frac{19}{5}=3.8). We round up to (w = 4).

Step3: Define classes

The first class starts at 0. The classes are (0 - 3), (4 - 7), (8 - 11), (12 - 15), (16 - 19).

Step4: Calculate frequencies

• For the class (0 - 3): The values in this class are (0,0,1,1,2,3), so the frequency (f_1=6).
• For the class (4 - 7): The values are (5,6,7,7,7), so the frequency (f_2 = 5).
• For the class (8 - 11): The values are (8,8,11,11), so the frequency (f_3=4).
• For the class (12 - 15): There are no values in this class, so the frequency (f_4 = 0).
• For the class (16 - 19): The values are (18,18,19), so the frequency (f_5=3).

Step5: Calculate mid - points

• For the class (0 - 3), the mid - point (x_1=\frac{0 + 3}{2}=1.5).
• For the class (4 - 7), the mid - point (x_2=\frac{4+7}{2}=5.5).
• For the class (8 - 11), the mid - point (x_3=\frac{8 + 11}{2}=9.5).
• For the class (12 - 15), the mid - point (x_4=\frac{12+15}{2}=13.5).
• For the class (16 - 19), the mid - point (x_5=\frac{16 + 19}{2}=17.5).

Step6: Calculate relative frequencies

The total frequency (N=f_1 + f_2+f_3+f_4+f_5=6 + 5+4+0+3=18).

• The relative frequency for the class (0 - 3) is (rf_1=\frac{f_1}{N}=\frac{6}{18}=\frac{1}{3}).
• The relative frequency for the class (4 - 7) is (rf_2=\frac{f_2}{N}=\frac{5}{18}).
• The relative frequency for the class (8 - 11) is (rf_3=\frac{f_3}{N}=\frac{4}{18}=\frac{2}{9}).
• The relative frequency for the class (12 - 15) is (rf_4=\frac{f_4}{N}=0).
• The relative frequency for the class (16 - 19) is (rf_5=\frac{f_5}{N}=\frac{3}{18}=\frac{1}{6}).

Step7: Calculate cumulative frequencies

• The cumulative frequency for the class (0 - 3) is (cf_1=f_1 = 6).
• The cumulative frequency for the class (4 - 7) is (cf_2=f_1 + f_2=6 + 5 = 11).
• The cumulative frequency for the class (8 - 11) is (cf_3=f_1 + f_2+f_3=6 + 5+4 = 15).
• The cumulative frequency for the class (12 - 15) is (cf_4=f_1 + f_2+f_3+f_4=6 + 5+4+0 = 15).
• The cumulative frequency for the class (16 - 19) is (cf_5=f_1 + f_2+f_3+f_4+f_5=6 + 5+4+0+3 = 18).

Class	Frequency	Mid - point	Relative Frequency	Cumulative Frequency
(0 - 3)	6	1.5	(\frac{1}{3})	6
(4 - 7)	5	5.5	(\frac{5}{18})	11
(8 - 11)	4	9.5	(\frac{2}{9})	15
(12 - 15)	0	13.5	0	15
(16 - 19)	3	17.5	(\frac{1}{6})	18

The class with the greatest frequency is (0 - 3) and the class with the least frequency is (12 - 15).

Answer:

Class	Frequency	Mid - point	Relative Frequency	Cumulative Frequency
(0 - 3)	6	1.5	(\frac{1}{3})	6
(4 - 7)	5	5.5	(\frac{5}{18})	11
(8 - 11)	4	9.5	(\frac{2}{9})	15
(12 - 15)	0	13.5	0	15
(16 - 19)	3	17.5	(\frac{1}{6})	18
The class with the greatest frequency is (0 - 3). The class with the least frequency is (12 - 15).