Table 4.2 (Distribution of 542 respondents by age in an election study in Bihar) leaves two cells blank for you to work out: the number of respondents (and their per cent) in the 60–70 age group, and the 'All' row's total number of respondents and per cent. Calculate the missing

Question

Table 4.2 (Distribution of 542 respondents by age in an election study in Bihar) leaves two cells blank for you to work out: the number of respondents (and their per cent) in the 60–70 age group, and the 'All' row's total number of respondents and per cent. Calculate the missing figures in the table.

Accepted Answer

> [!TLDR]
> The 60–70 age group has **140 respondents (25.83%)**, and the **All row totals 542 respondents (100.00%)** — both follow from the fact that every column of a frequency table must sum to the stated total.

## Concept first: a frequency table's own totals are a built-in check

In a tabulated frequency distribution, the individual class frequencies must always add up to the grand total the table (or the surrounding text) states — here, Table 4.2 is explicitly a **distribution of 542 respondents**. That known total is what lets a reader fill in a blank cell without re-surveying anyone.

## Step 1 — add up the six known age groups

| Age group | Respondents |
|---|---|
| 20–30 | 3 |
| 30–40 | 61 |
| 40–50 | 132 |
| 50–60 | 153 |
| 70–80 | 51 |
| 80–90 | 2 |
| **Sum** | **402** |

$$3+61+132+153+51+2 = 402$$

## Step 2 — the 60–70 group makes up the rest of 542

$$542 - 402 = 140 	ext{ respondents}$$ …

Age group	Respondents
20–30	3
30–40	61
40–50	132
50–60	153
70–80	51
80–90	2
Sum	402

Concept first: a frequency table's own totals are a built-in check

Step 1 — add up the six known age groups

Step 2 — the 60–70 group makes up the rest of 542

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