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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.
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.
Solution :
Given: A frequency distribution of the number of heartbeats per minute for 30 women.
To Find: The mean number of heartbeats per minute using a suitable method.
Data Table:
| Number of heartbeats per minute (Class Interval) | Number of women ($f_i$) |
|---|---|
| 65 - 68 | 2 |
| 68 - 71 | 4 |
| 71 - 74 | 3 |
| 74 - 77 | 8 |
| 77 - 80 | 7 |
| 80 - 83 | 4 |
| 83 - 86 | 2 |
Method Selection: Since the class intervals are uniform and the values are manageable, we will use the Assumed Mean Method to calculate the mean ($\bar{x}$).
Formula: $\bar{x} = a + \frac{\sum f_i d_i}{\sum f_i}$, where $a$ is the assumed mean and $d_i = x_i - a$.
Step 1: Constructing the Calculation Table
| Class Interval | Frequency ($f_i$) | Class Mark ($x_i$) | Deviation ($d_i = x_i - a$) | $f_i d_i$ |
|---|---|---|---|---|
| 65 - 68 | 2 | 66.5 | -9 | -18 |
| 68 - 71 | 4 | 69.5 | -6 | -24 |
| 71 - 74 | 3 | 72.5 | -3 | -9 |
| 74 - 77 | 8 | 75.5 (a) | 0 | 0 |
| 77 - 80 | 7 | 78.5 | 3 | 21 |
| 80 - 83 | 4 | 81.5 | 6 | 24 |
| 83 - 86 | 2 | 84.5 | 9 | 18 |
| Total | $\sum f_i = 30$ | - | - | $\sum f_i d_i = 12$ |
Step 2: Defining Variables
Let the assumed mean $a = 75.5$.
The class size $h = 68 - 65 = 3$.
The sum of frequencies $\sum f_i = 30$.
The sum of deviations $\sum f_i d_i = (-18) + (-24) + (-9) + 0 + 21 + 24 + 18 = 12$.
Step 3: Applying the Formula
$\bar{x} = a + \frac{\sum f_i d_i}{\sum f_i}$
$\bar{x} = 75.5 + \frac{12}{30}$ [Substituting the values]
$\bar{x} = 75.5 + 0.4$ [Simplifying the fraction $12/30 = 2/5 = 0.4$]
$\bar{x} = 75.9$
Final Answer: The mean number of heartbeats per minute for these women is 75.9.
More Questions from Class 10 Mathematics Statistics EXERCISE 13.1
- 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?
- 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 $f$.
- 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
Chapters in CBSE - Class 10 Mathematics
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