A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.
| Number of plants | 0 - 2 | 2 - 4 | 4 - 6 | 6 - 8 | 8 - 10 | 10 - 12 | 12 - 14 |
|---|---|---|---|---|---|---|---|
| Number of houses | 1 | 2 | 1 | 5 | 6 | 2 | 3 |
Which method did you use for finding the mean, and why?
To find the mean number of plants per house, we use the Direct Method.
First, we calculate the class mark () for each interval, which is the midpoint of the class. Then, we compute the product of frequency and class mark ().
| Number of plants | Number of houses () | Class mark () | |
|---|---|---|---|
| 0 - 2 | 1 | 1 | 1 |
| 2 - 4 | 2 | 3 | 6 |
| 4 - 6 | 1 | 5 | 5 |
| 6 - 8 | 5 | 7 | 35 |
| 8 - 10 | 6 | 9 | 54 |
| 10 - 12 | 2 | 11 | 22 |
| 12 - 14 | 3 | 13 | 39 |
| Total |
Mean
Method Used: I used the Direct Method because the class sizes were small and the values of the class marks () were small integers. This made the calculation of simple and manageable without needing to assume a mean or use the step-deviation method.
Explanation
The question requires finding the mean from a grouped frequency distribution. The Direct Method is chosen because the numerical values involved (class marks and frequencies) are small integers, making direct computation straightforward and less prone to calculation errors compared to methods involving assumed means. The solution involves finding the midpoint (class mark) for each interval, multiplying it by the frequency, summing these products, and dividing by the total frequency.
Solution Steps
Step 1: Identify the class intervals and frequencies () from the given data.
Step 2: Calculate the class mark () for each interval by finding the midpoint (e.g., for 0-2, ).
Step 3: Calculate the product for each row (e.g., for the first row, ).
Step 4: Sum the frequencies to get and sum the products to get .
Step 5: Apply the Direct Method formula: Mean .