Question

a class had students keep track of their social interactions for a week. the number of
interactions over the week is shown in the grouped frequency distribution table to
right. how many students were involved in this study?
the number of students was
(type a whole number.)
number of social
interactions
frequency
20 - 26
19
27 - 33
12
34 - 40
19
41 - 47
10
48 - 54
15
55 - 61
12
62 - 68
4
69 - 75
8
76 - 82
1
83 - 89
3

Explanation:

Step1: Identify all frequencies

The frequencies for each class interval are: 19, 12, 19, 10, 15, 12, 4, 8, 1, 3. Wait, wait, let's check the table again. Wait, the first row of frequencies (from the image, let's parse the numbers properly). Let's list the frequencies: 19 (for 20-26), 12 (27-33), 19 (34-40), 10 (41-47), 15 (48-54), 12 (55-61), 4 (62-68), 8 (69-75), 1 (76-82), 3 (83-89). Wait, no, maybe I misread. Wait, the original table (from the image) has:

Number of Social Interactions: 20-26, 27-33, 34-40, 41-47, 48-54, 55-61, 62-68, 69-75, 76-82, 83-89

Frequencies: 19, 12, 19, 10, 15, 12, 4, 8, 1, 3. Wait, no, maybe the first frequency is 19? Wait, no, let's add all frequencies. Let's list them correctly:

Wait, the user's image: let's extract the frequencies. Let's see the numbers:

First frequency (20-26): 19? Wait, no, maybe the first is 19? Wait, no, let's check again. Wait, the numbers are: 19, 12, 19, 10, 15, 12, 4, 8, 1, 3. Wait, no, maybe I made a mistake. Wait, let's add them step by step.

Wait, let's list all frequencies:

• 20-26: 19

• 27-33: 12

• 34-40: 19

• 41-47: 10

• 48-54: 15

• 55-61: 12

• 62-68: 4

• 69-75: 8

• 76-82: 1

• 83-89: 3

Now, sum all these frequencies.

Step2: Sum the frequencies

Sum = 19 + 12 + 19 + 10 + 15 + 12 + 4 + 8 + 1 + 3

Let's calculate step by step:

19 + 12 = 31

31 + 19 = 50

50 + 10 = 60

60 + 15 = 75

75 + 12 = 87

87 + 4 = 91

91 + 8 = 99

99 + 1 = 100

100 + 3 = 103? Wait, no, wait: 19+12=31; 31+19=50; 50+10=60; 60+15=75; 75+12=87; 87+4=91; 91+8=99; 99+1=100; 100+3=103? Wait, no, maybe I misread the frequencies. Wait, maybe the first frequency is 19? Wait, no, let's check again. Wait, maybe the frequencies are: 19, 12, 19, 10, 15, 12, 4, 8, 1, 3. Wait, but 19+12=31, +19=50, +10=60, +15=75, +12=87, +4=91, +8=99, +1=100, +3=103. Wait, but maybe I made a mistake in the frequencies. Wait, maybe the first frequency is 19? Wait, no, let's check the original problem again. Wait, the user's image: the frequencies are:

Wait, the first row (Number of Social Interactions) has 20-26, 27-33, 34-40, 41-47, 48-54, 55-61, 62-68, 69-75, 76-82, 83-89.

The second row (Frequency) has: 19, 12, 19, 10, 15, 12, 4, 8, 1, 3.

Wait, but let's add them again:

19 (20-26) + 12 (27-33) = 31

31 + 19 (34-40) = 50

50 + 10 (41-47) = 60

60 + 15 (48-54) = 75

75 + 12 (55-61) = 87

87 + 4 (62-68) = 91

91 + 8 (69-75) = 99

99 + 1 (76-82) = 100

100 + 3 (83-89) = 103. Wait, but that seems off. Wait, maybe I misread the frequencies. Wait, maybe the first frequency is 19? Wait, no, maybe the numbers are different. Wait, maybe the frequencies are: 19, 12, 19, 10, 15, 12, 4, 8, 1, 3. Wait, but let's check again. Wait, maybe the 34-40 frequency is 19? Wait, no, maybe the user made a typo, but assuming the frequencies are as listed, the sum is 103? Wait, no, wait, let's add again:

19 + 12 = 31

31 + 19 = 50

50 + 10 = 60

60 + 15 = 75

75 + 12 = 87

87 + 4 = 91

91 + 8 = 99

99 + 1 = 100

100 + 3 = 103. So the total number of students is 103.

Answer:

103