Two-Way Frequency Table Completion with Missing Values

Published on March 6, 2026

Statistics

Calculate the missing entries in a two-way contingency table by using row and column totals, a fundamental skill in data analysis and statistics.

Question

This problem requires filling in the missing values in a two-way frequency table based on the given marginal totals.

Let’s represent the table with variables for the missing values:

Grade	Less	Total
7th grade	28	47
8th grade
Total	51	84

We use the principle that the sum of the values in a row or a column equals the total for that row or column.

Step 1: Find the missing value in the 7th grade row (A).
For the 7th grade row:

So, the number of 7th graders who spend more than an hour is 19.

Step 2: Find the missing value in the Total row (E).
For the “More” column:

We also know the grand total is 84, and the total for the “Less” column is 51.
For the Total row:

So, the total number of students who spend more than an hour is 33.

Step 3: Find the missing value in the 8th grade “More” category (B).
For the “More” column:

So, the number of 8th graders who spend more than an hour is 14.

Step 4: Find the missing value in the Total row (D).
For the Grand Total:

So, the total number of 8th graders is 37.

Step 5: Find the missing value in the 8th grade “Less” category ©.
For the 8th grade row:

Alternatively, using the “Less” column:

Both methods yield

Summary of Missing Values:

The completed table is:

Grade	More	Less	Total
7th grade	19	28	47
8th grade	14	23	37
Total	33	51	84

The missing values are 19 (7th grade More), 14 (8th grade More), 23 (8th grade Less), 37 (8th grade Total), and 33 (Total More).

If the required output is the list of missing values in order of appearance (row by row, left to right for the blank cells):

The missing values are 19, 14, 23, 37, and 33.