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How to build a frequency table from raw data

Count once, then check the total

A frequency is the number of times one value appears. Make a tally for each distinct value, then add all frequencies. The sum must equal the number of observations. That total check is necessary, although it cannot by itself catch every pair of counting errors.

Problem

Forty students reported hours spent on homework in one week. Make a frequency table for: 5; 1.5; 0; 2.5; 1; 0; 0; 2; 2.5; 3.5; 4; 5; 3.5; 2.5; 0; 1.5; 4.5; 3; 3; 5; 3.5; 4; 3.5; 3; 2.5; 2; 1; 2; 2; 4.5; 4; 3.5; 2; 5; 4; 2; 2.5; 0; 0; 3.

Answer

Frequencies:

0 : 6

1 : 2

1.5 : 2

2 : 6

2.5 : 5

3 : 4

3.5 : 5

4 : 4

4.5 : 2

5 : 4

Each value was recounted from the original 40 observations; the source AI answer had incorrect counts.

Step-by-step solution

1. List the distinct values

The recorded times are $0$ , $1$ , $1.5$ , $2$ , $2.5$ , $3$ , $3.5$ , $4$ , $4.5$ and $5$ hours.

2. Tally each occurrence

Reading the original list from left to right gives these frequencies:

0 : 6, 1 : 2, 1.5 : 2, 2 : 6, 2.5 : 5,

3 : 4, 3.5 : 5, 4 : 4, 4.5 : 2, 5 : 4.

For example, zero appears six times, and five hours appears four times.

3. Check the number of observations

6 + 2 + 2 + 6 + 5 + 4 + 5 + 4 + 2 + 4 = 40.

The frequency total matches the 40 students. When preparing a table, also recheck the individual tallies: a correct total alone could hide an overcount paired with an undercount.

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