The weights (in kg) of 50 wild animals of a National Park were recorded and the following data was obtained. Find the mean weight (in kg) of animals, using assumed mean method.
Generated by claude-sonnet-4-6 · 2026-06-15 10:34 · grounding rag
Model Answer
Let assumed mean a = 125, class size h = 10.
| Weight (kg) | $f_i$ | $x_i$ | $d_i = x_i - 125$ | $f_i d_i$ |
|---|---|---|---|---|
| 100–110 | 4 | 105 | –20 | –80 |
| 110–120 | 12 | 115 | –10 | –120 |
| 120–130 | 23 | 125 | 0 | 0 |
| 130–140 | 8 | 135 | 10 | 80 |
| 140–150 | 3 | 145 | 20 | 60 |
| Total | 50 | | | –60 |
$$\bar{x} = a + \frac{\Sigma f_i d_i}{\Sigma f_i} = 125 + \frac{-60}{50} = 125 - 1.2 = \mathbf{123.8 \text{ kg}}$$
Mean weight of animals = 123.8 kg
Source: Chapter 13, Section 13.2 (Assumed Mean Method)
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Explanation
- Choose assumed mean a = 125 (midpoint of the middle class 120–130, which has the highest frequency — a natural central value).
- Calculate deviations $d_i = x_i - a$ for each class mark.
- Apply the formula: $\bar{x} = a + \dfrac{\Sigma f_i d_i}{\Sigma f_i}$.
- Examiners award marks for: correct table with $f_i$, $x_i$, $d_i$, $f_id_i$; correct $\Sigma f_i = 50$ and $\Sigma f_id_i = -60$; and correct final calculation.
- Note the negative sum of $f_id_i$ — don't drop the minus sign.