Question

(c) raw data of number of messages: 10 12 16 6 5 6 18 14 8 20 8 9 2 15 7 11 12 9 19 8
number of messages frequency
1 to 5
6 to 10
11 to 15
16 to 20
(f) raw data of time in minutes for 5k race: 32 29 25 39 42 21 44 35 27 29 33 31 37 28 33 40 34 29
time (minutes) frequency
20 ≤ t < 25
25 ≤ t < 30
30 ≤ t < 35
35 ≤ t < 40
40 ≤ t < 45

Explanation:

Step1: Count for messages 1 - 5

The values in the range 1 - 5 in the message - data are 5, 2. So the frequency is 2.

Step2: Count for messages 6 - 10

The values in the range 6 - 10 are 10, 6, 6, 8, 8, 9, 9, 8. So the frequency is 8.

Step3: Count for messages 11 - 15

The values in the range 11 - 15 are 12, 14, 11, 12, 15. So the frequency is 5.

Step4: Count for messages 16 - 20

The values in the range 16 - 20 are 16, 18, 20, 19. So the frequency is 4.

Step5: Count for time 20 ≤ t < 25

The values in the range 20 ≤ t < 25 in the time - data are 21, 25. So the frequency is 2.

Step6: Count for time 25 ≤ t < 30

The values in the range 25 ≤ t < 30 are 29, 25, 27, 29, 28, 29. So the frequency is 6.

Step7: Count for time 30 ≤ t < 35

The values in the range 30 ≤ t < 35 are 32, 33, 31, 33, 34. So the frequency is 5.

Step8: Count for time 35 ≤ t < 40

The values in the range 35 ≤ t < 40 are 39, 35, 37. So the frequency is 3.

Step9: Count for time 40 ≤ t < 45

The values in the range 40 ≤ t < 45 are 42, 44, 40. So the frequency is 3.

Answer:

Number of Messages	Frequency
6 to 10	8
11 to 15	5
16 to 20	4

Time (minutes)	Frequency
25 ≤ t < 30	6
30 ≤ t < 35	5
35 ≤ t < 40	3
40 ≤ t < 45	3