Question

Имеются данные о распределении коммерческих банков по величине активов: Активы, млрд. руб. Число банков До 100 20 100 -200 31 200 -300 18 300-400 16 400-500 15 500 и более 13 Итого 113 Определите средний размер активов.

Answer 1

262.39 ср.размер активов по ср.арифметической взвешенной

Answer 2

Calculation of Average Asset Size of Commercial Banks

To determine the average size of assets for the given distribution of commercial banks, we need to calculate the weighted average based on the number of banks in each asset range.

Here is the distribution of commercial banks by asset size:

| Asset Range (in billion rubles) | Number of Banks | |---------------------------------|-----------------| | Up to 100 | 20 | | 100 - 200 | 31 | | 200 - 300 | 18 | | 300 - 400 | 16 | | 400 - 500 | 15 | | 500 and above | 13 | | Total | 113 |

To calculate the average asset size, we need to multiply the midpoint of each asset range by the number of banks in that range, sum up the results, and then divide by the total number of banks.

Let's perform the calculations:

- For the asset range "Up to 100": - Midpoint: (0 + 100) / 2 = 50 - Number of banks: 20 - Contribution: 50 * 20 = 1000

- For the asset range "100 - 200": - Midpoint: (100 + 200) / 2 = 150 - Number of banks: 31 - Contribution: 150 * 31 = 4650

- For the asset range "200 - 300": - Midpoint: (200 + 300) / 2 = 250 - Number of banks: 18 - Contribution: 250 * 18 = 4500

- For the asset range "300 - 400": - Midpoint: (300 + 400) / 2 = 350 - Number of banks: 16 - Contribution: 350 * 16 = 5600

- For the asset range "400 - 500": - Midpoint: (400 + 500) / 2 = 450 - Number of banks: 15 - Contribution: 450 * 15 = 6750

- For the asset range "500 and above": - Midpoint: (500 + ∞) / 2 = ∞ (approximated as 1000 for calculation purposes) - Number of banks: 13 - Contribution: 1000 * 13 = 13000

Now, let's sum up the contributions and divide by the total number of banks:

Total contribution = 1000 + 4650 + 4500 + 5600 + 6750 + 13000 = 44400

Average asset size = Total contribution / Total number of banks = 44400 / 113 ≈ 392.92 billion rubles

Therefore, the average size of assets for the given distribution of commercial banks is approximately 392.92 billion rubles.