Question
Calculate arithmetic mean with the help of following data using step deviation method.
| Marks (Less than) | 10 | 20 | 30 | 40 | 50 | 60 |
| Number of Students | 3 | 10 | 20 | 25 | 28 | 30 |
| Marks (Less than) | 10 | 20 | 30 | 40 | 50 | 60 |
| Number of Students | 3 | 10 | 20 | 25 | 28 | 30 |
The given data is less than type hence, first of all convert the less than cumulative frequency series into an ordinary series and then calculate the value of arithmetic mean. For the calculation of Arithmetic Mean let A =25
Calculation of Arithmetic Mean using step deviation method
| Marks | Frequency (f) | Mid-Value (m) m=(L1+L2)/2 | dm=m-A (A=25) | $\begin{array}{l}d^{\prime} m=\frac{d m}{c} \\ ( c = 1 0 ) \end{array}$ | fd'm |
| 0-10 | 3 | 5 | -20 | -2 | -6 |
| 10-20 | 10-3=7 | 15 | -10 | -1 | -7 |
| 20-30 | 20-10=10 | 25 | 0 | 0 | 0 |
| 30-40 | 25-20=5 | 35 | +10 | +1 | +5 |
| 40-50 | 28-25=3 | 45 | +20 | +2 | +6 |
| 50-60 | 30-28=2 | 55 | +30 | +3 | +6 |
| $\Sigma f=30$ | $\Sigma f d^{\prime} m=+4$ |
Here,
$
\begin{array}{l}
A=25, \Sigma f=30, \Sigma f d^{\prime} m=+4, c=10 \\
\text { Now, } \bar{X}=A+\frac{\Sigma f d^{\prime} m}{\Sigma f} \times c=25+\frac{4}{30} \times 10 \\
=25+1.33=26.33
\end{array}
$
Therefore,arithmetic mean of the given data is 26.33
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| Output (units) | Price (₹) | Total Cost (₹) |
| 1 | 12 | 14 |
| 2 | 12 | 26 |
| 3 | 12 | 35 |
| 4 | 12 | 52 |
| 5 | 12 | 64 |
| 6 | 12 | 70 |
| Output (units) |
Average fixed cost (Rs.) |
Marginal cost (Rs.) |
| 1 | 60 | 32 |
| 2 | 30 | 30 |
| 3 | 20 | 28 |
| 4 | 15 | 30 |
| 5 | 12 | 35 |
| 6 | 10 | 43 |