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The following are the monthly rents (in rupees) of 40 shops:

3800, 4200, 4900, 3700, 7500, 6200, 5400, 7900, 8400, 7500, 6300, 4400, 7400, 4400, 3600, 6900, 5400, 4800, 3700, 7400, 3900, 4800, 4500, 6100, 4700, 7100, 4700, 3800, 8000, 5100, 3100, 3800, 4300, 7500, 6700, 8200, 7700, 6400, 8400, 8100.

Using class intervals like 3000-3800 and 3800-4600, construct a frequency table for the above data using tally marks.

Also, prepare a cumulative frequency column.

Using the data from the above question, calculate the mean monthly rent of the 40 shops (in rupees).

Answer :

Final Answer:

The mean monthly rent of the 40 shops is approximately 5967.5 rupees.

Explanation:

To find the mean monthly rent, we need to follow these steps. First, we construct a frequency table using class intervals and tally marks based on the given data. Then, we calculate the cumulative frequency for each class interval.

Finally, we use the formula for the mean, which is the sum of (midpoint of class interval * frequency) divided by the total frequency.

The frequency table for the given data is as follows:

| Class Interval | Tally | Frequency | Cumulative Frequency |

|----------------|-------|-----------|---------------------|

| 3000-3800 | || 4 | 4 |

| 3800-4600 | || 6 | 10 |

| 4600-5400 | || 8 | 18 |

| 5400-6200 | || 6 | 24 |

| 6200-7000 | || 7 | 31 |

| 7000-7800 | || 4 | 35 |

| 7800-8600 | || 5 | 40 |

Now, let's calculate the cumulative frequency and midpoint for each class interval and use them to find the mean monthly rent:

- Cumulative Frequency for 3000-3800: 4

- Cumulative Frequency for 3800-4600: 10

- Cumulative Frequency for 4600-5400: 18

- Cumulative Frequency for 5400-6200: 24

- Cumulative Frequency for 6200-7000: 31

- Cumulative Frequency for 7000-7800: 35

- Cumulative Frequency for 7800-8600: 40

The sum of (midpoint * frequency) for each interval is:

(3400 * 4) + (4200 * 6) + (5000 * 8) + (5800 * 6) + (6600 * 7) + (7400 * 4) + (8200 * 5) = 238800

The total frequency is 40.

Mean = (Sum of (midpoint * frequency)) / Total Frequency = 238800 / 40 = 5970

Therefore, the mean monthly rent of the 40 shops is approximately 5967.5 rupees.

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