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Select the table that shows the correct cumulative relative frequencies for the data in the following table:

upper x Frequency Relative Frequency
0 35 0.07
1 120 0.24
2 90 0.18
3 170 0.34
4 85 0.17
(1 point)
Responses

upper x Frequency Relative Frequency Cumulative Relative Frequency
0 35 0.07 35
1 120 0.24 155
2 90 0.18 245
3 170 0.34 415
4 85 0.17 500
Image with alt text: upper x Frequency Relative Frequency Cumulative Relative Frequency 0 35 0.07 35 1 120 0.24 155 2 90 0.18 245 3 170 0.34 415 4 85 0.17 500

upper x Frequency Relative Frequency& Cumulative Relative Frequency
0 35 0.07 0.07
1 120 0.24 0.31
2 90 0.18 0.49
3 170 0.34 0.83
4 85 0.17 1.00
Image with alt text: upper x Frequency Relative Frequency& Cumulative Relative Frequency 0 35 0.07 0.07 1 120 0.24 0.31 2 90 0.18 0.49 3 170 0.34 0.83 4 85 0.17 1.00

upper x Frequency Relative Frequency Cumulative Relative Frequency
0 35 0.07 1.00
1 120 0.24 0.93
2 90 0.18 0.69
3 170 0.34 0.51
4 85 0.17 0.17
Image with alt text: upper x Frequency Relative Frequency Cumulative Relative Frequency 0 35 0.07 1.00 1 120 0.24 0.93 2 90 0.18 0.69 3 170 0.34 0.51 4 85 0.17 0.17

upper x Frequency Relative Frequency Cumulative Relative Frequency
0 35 0.07 0.17
1 120 0.24 0.34
2 90 0.18 0.18
3 170 0.34 0.24
4 85 0.17 0.07
Image with alt text: upper x Frequency Relative Frequency Cumulative Relative Frequency 0 35 0.07 0.17 1 120 0.24 0.34 2 90 0.18 0.18 3 170 0.34 0.24 4 85 0.17 0.07

1 answer

To find the correct cumulative relative frequencies, we begin by calculating the cumulative relative frequency using the relative frequencies provided.

The relative frequencies for each class are as follows:

  • \(R_0 = 0.07\)
  • \(R_1 = 0.24\)
  • \(R_2 = 0.18\)
  • \(R_3 = 0.34\)
  • \(R_4 = 0.17\)

Now, let's calculate the cumulative relative frequency step by step:

  1. For \(x = 0\):

    • Cumulative Relative Frequency \(C_0 = R_0 = 0.07\)

  2. For \(x = 1\):

    • Cumulative Relative Frequency \(C_1 = C_0 + R_1 = 0.07 + 0.24 = 0.31\)

  3. For \(x = 2\):

    • Cumulative Relative Frequency \(C_2 = C_1 + R_2 = 0.31 + 0.18 = 0.49\)

  4. For \(x = 3\):

    • Cumulative Relative Frequency \(C_3 = C_2 + R_3 = 0.49 + 0.34 = 0.83\)

  5. For \(x = 4\):

    • Cumulative Relative Frequency \(C_4 = C_3 + R_4 = 0.83 + 0.17 = 1.00\)

Now, compiling this information gives us the following cumulative relative frequencies:

  • For \(x = 0\): \(0.07\)
  • For \(x = 1\): \(0.31\)
  • For \(x = 2\): \(0.49\)
  • For \(x = 3\): \(0.83\)
  • For \(x = 4\): \(1.00\)

Now, we compare our calculations with the options given. The correct table of cumulative relative frequencies is:

upper x   Frequency   Relative Frequency   Cumulative Relative Frequency
0         35          0.07                 0.07
1         120         0.24                 0.31
2         90          0.18                 0.49
3         170         0.34                 0.83
4         85          0.17                 1.00

Thus, the correct response is the second option displayed in the problem statement.