College

A random sample of the body temperature of 25 young adults has the following distribution. Complete the table by filling in the cumulative frequency distribution.

[tex]
\[
\begin{tabular}{|c|c|c|}
\hline
\text{Temperature Group} & \text{Frequency} & \text{Cumulative Frequency} \\
\hline
$96-96.4$ & 3 & $\square$ \\
\hline
$96.5-96.9$ & 5 & $\square$ \\
\hline
$97-97.4$ & 3 & $\square$ \\
\hline
$97.5-97.9$ & 3 & $\square$ \\
\hline
$98-98.4$ & 8 & $\square$ \\
\hline
$98.5-98.9$ & 2 & \\
\hline
$99-99.4$ & 1 & \\
\hline
\end{tabular}
\]
[/tex]

Answer :

To complete the cumulative frequency distribution table, we need to add up the frequencies as we move down each temperature group.

Cumulative frequency is essentially a running total of frequencies through the classes in the table. This means for each class, you add the frequency of the current class to the cumulative total of the previous classes.

Let's calculate the cumulative frequency for each temperature group:

  1. Temperature Group: $96-96.4$

    • Frequency: 3
    • Cumulative Frequency: 3 (since this is the first group, cumulative is the same as the frequency)

  2. Temperature Group: $96.5-96.9$

    • Frequency: 5
    • Cumulative Frequency: 3 + 5 = 8

  3. Temperature Group: $97-97.4$

    • Frequency: 3
    • Cumulative Frequency: 8 + 3 = 11

  4. Temperature Group: $97.5-97.9$

    • Frequency: 3
    • Cumulative Frequency: 11 + 3 = 14

  5. Temperature Group: $98-98.4$

    • Frequency: 8
    • Cumulative Frequency: 14 + 8 = 22

  6. Temperature Group: $98.5-98.9$

    • Frequency: 2
    • Cumulative Frequency: 22 + 2 = 24

  7. Temperature Group: $99-99.4$

    • Frequency: 1
    • Cumulative Frequency: 24 + 1 = 25

The cumulative frequency for the last group should equal the total number of observations in the sample, which is 25 in this case. By checking the cumulative frequency for the last group, we can see that the calculations are correct.

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