Lifetime (days) 0-10 10-20 20-30 30-40 40-50 50-60 Frequency 10 35 52 61 38 29
The question asks us to calculate the modal lifetime from the given frequency distribution table. The modal lifetime represents the most frequent lifetime range in the data.
Identifying the Modal Class
First, we need to identify the modal class, which is the class interval with the highest frequency.
| Lifetime (days) | Frequency |
|---|---|
| 0-10 | 10 |
| 10-20 | 35 |
| 20-30 | 52 |
| 30-40 | 61 |
| 40-50 | 38 |
| 50-60 | 29 |
From the table, the highest frequency is 61, which corresponds to the lifetime interval 30-40 days. Therefore, the modal class is 30-40.
Modal Lifetime Calculation Formula
We use the formula for calculating the mode of grouped data:
Mode = \(l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h\)
Where:
- \(l\) = Lower limit of the modal class
- \(f_1\) = Frequency of the modal class
- \(f_0\) = Frequency of the class preceding the modal class
- \(f_2\) = Frequency of the class succeeding the modal class
- \(h\) = Class width
Applying the Formula
From the identified modal class (30-40):
- \(l = 30\)
- \(f_1 = 61\)
- \(f_0 = 52\) (Frequency of the 20-30 class)
- \(f_2 = 38\) (Frequency of the 40-50 class)
- \(h = 10\) (Class width, e.g., 40 - 30 = 10)
Substitute these values into the formula:
Mode = \(30 + \frac{61 - 52}{2 \times 61 - 52 - 38} \times 10\)
Mode = \(30 + \frac{9}{122 - 52 - 38} \times 10\)
Mode = \(30 + \frac{9}{122 - 90} \times 10\)
Mode = \(30 + \frac{9}{32} \times 10\)
Mode = \(30 + \frac{90}{32}\)
Mode = \(30 + 2.8125\)
Mode = \(32.8125\)
Rounding the Result
The question requires the answer to be rounded up to one decimal place. Rounding 32.8125 gives 32.8.
Therefore, the modal lifetime is approximately 32.8 days.
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Important Questions from Elementary Statistics
What is the mode of the given data?
3, 0, 1, 0, 2, 1, 2, 0, 1, 2, 1, 1, 1, 3, 2What is the mode of the given data?
21, 22, 23, 23, 24, 21, 22, 23, 21, 23, 24, 23, 21, 23A bowler has taken 0, 3, 2, 1, 5, 3, 4, 5, 5, 2, 2, 0, 0, 1 and 2 wickets in 15 consecutive matches. What is the mode of the given data?
The data given below shows the number of people who have saved a certain amount of money.
Saving (In Rs.)
Number of people
5
1
15
3
20
4
25
2
30
1
35
1
40
2
What is the median of the given data?
If the ratio of mean and median of a certain data is 4 : 5, then find the ratio of its mean and mode.
