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The batting average $\text{(BA)}$ of a test batsman is computed from runs scored and innings played-completed innings and incomplete innings (not out) in the following manner:

  • $r_1$ = number of runs scored in completed innings;
  • $n_1$ = number of completed innings
  • $r_2$ = number of runs scored in incomplete innings;
  • $n_2$ = number of incomplete innings 
  • $\text{BA} =\frac{r_1 + r_2}{n_1}$

To better assess batsman's accomplishments, the ICC is considering two other measures $\text{MBA}_1$ and $\text{MBA}_2$ defined as follows:

  • $\text{MBA}_1 = \frac{r_1}{n_1} + \frac{n_2}{n_1} \: \: \max\left[0, \left(\frac{r_2}{n_2} - \frac{r_1}{n_1}\right)\right]$
  • $\text{MBA}_2 = \frac{r_1 + r_2}{n_1 + n_2}$

Based on the information provided which of the following is true?

  1. $\text{MBA}_1 \leq \text{BA} \leq \text{MBA}_2$
  2. $\text{BA} \leq \text{MBA}_2 \leq \text{MBA}_1$
  3. $\text{MBA}_2 \leq \text{BA} \leq \text{MBA}_1$
  4. None of these


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