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Q1:
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.
Which method did you use for finding the mean, and why?
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.
Which method did you use for finding the mean, and why?
Solution :
Given: A frequency distribution table representing the number of plants in 20 houses.
| Number of plants | 0-2 | 2-4 | 4-6 | 6-8 | 8-10 | 10-12 | 12-14 |
|---|---|---|---|---|---|---|---|
| Number of houses ($f_i$) | 1 | 2 | 1 | 5 | 6 | 2 | 3 |
To Find: The mean number of plants per house and the justification for the chosen method.
Step 1: Choosing the Method
Since the class intervals are small and the frequencies are manageable, we will use the Direct Method to calculate the mean. The formula for the mean ($\bar{x}$) using the direct method is:
$\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$
where $x_i$ is the class mark of each interval.
Step 2: Constructing the Calculation Table
We calculate the class mark ($x_i$) for each interval using the formula: $x_i = \frac{\text{Upper Limit} + \text{Lower Limit}}{2}$.
| Number of plants (Class Interval) | Number of houses ($f_i$) | Class mark ($x_i$) | $f_i \times x_i$ |
|---|---|---|---|
| 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 | $\sum f_i = 20$ | - | $\sum f_i x_i = 162$ |
Step 3: Calculating the Mean
Using the values obtained from the table:
$\sum f_i = 20$
$\sum f_i x_i = 1 + 6 + 5 + 35 + 54 + 22 + 39 = 162$
Substituting these into the mean formula:
$\bar{x} = \frac{162}{20}$
$\bar{x} = 8.1$
Step 4: Justification
The Direct Method was used because the numerical values of the class marks ($x_i$) and the frequencies ($f_i$) are small, making the multiplication $f_i x_i$ straightforward and easy to compute without the need for complex deviations or assumed mean methods.
Final Answer: The mean number of plants per house is 8.1.
More Questions from Class 10 Mathematics Statistics EXERCISE 13.1
- Q2: Consider the following distribution of daily wages of 50 workers of a factory. Find the mean daily wages of the workers of the factory by using an appropriate method.
- Q3: The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs 18. Find the missing frequency $f$.
- Q4: Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarised as follows. Find the mean heartbeats per minute for these women, choosing a suitable method.
- Q5: In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes. Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?
- Q6: The table below shows the daily expenditure on food of 25 households in a locality. Find the mean daily expenditure on food by a suitable method.
- Q7: To find out the concentration of $SO_2$ in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below: Find the mean concentration of $SO_2$ in the air.
- Q8: A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.
- Q9: The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
CBSE Solutions for Class 10 Mathematics Statistics
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