High School

Using the following frequency information, find the cumulative frequency of the class '40.5–43.5':

Temperature | Frequency
------------|---------
28.5 < x ≤ 31.5 | 1
31.5 < x ≤ 34.5 | 3
34.5 < x ≤ 37.5 | 6
37.5 < x ≤ 40.5 | 13
40.5 < x ≤ 43.5 | 8
43.5 < x ≤ 46.5 | 7
46.5 < x ≤ 49.5 | 2

Answer :

To find the cumulative frequency for the class '40.5–43.5,' we need to add up the frequencies of all classes up to and including that class. Here's how you can do it step-by-step:

  1. Identify the Frequencies: First, list the frequencies given for each class interval.

    • 28.5 < x ≤ 31.5: 1
    • 31.5 – 34.5: 3
    • 34.5 – 37.5: 6
    • 37.5 – 40.5: 13
    • 40.5 – 43.5: 8

  2. Sum the Frequencies: Add up frequencies up to and including the '40.5–43.5' class interval.

    [tex]\text{Cumulative frequency} = 1 + 3 + 6 + 13 + 8[/tex]

  3. Calculate the Total:

    [tex]= 1 + 3 + 6 + 13 + 8 = 31[/tex]

Therefore, the cumulative frequency for the class '40.5–43.5' is 31.

Cumulative frequency helps in understanding the distribution of data and how values accumulate across different intervals. This can be particularly useful in statistics to identify how data is spread across ranges.