Advertisements
Advertisements
Question
The monthly income of 100 families are given as below :
| Income in ( in ₹) | Number of families |
| 0-5000 | 8 |
| 5000-10000 | 26 |
| 10000-15000 | 41 |
| 15000-20000 | 16 |
| 20000-25000 | 3 |
| 25000-30000 | 3 |
| 30000-35000 | 2 |
| 35000-40000 | 1 |
Calculate the modal income.
Solution
The maximum class frequency is 41. The class corresponding to this frequency is 10000–15000.
So, the modal class is 10000–15000.
l (the lower limit of modal class) = 10000
f1 (frequency of the modal class) = 41
f0 (frequency of the class preceding the modal class) = 26
f2 (frequency of the class succeeding the modal class) = 16
h (class size) = 5000
\[\text{Mode }= l + \left( \frac{f_1 - f_0}{2 f_1 - f_0 - f_2} \right) \times h\]
\[ = 10000 + \left( \frac{41 - 26}{2 \times 41 - 26 - 16} \right) \times 5000\]
\[ = 10000 + \frac{15}{40} \times 5000\]
\[ = 10000 + 1875\]
\[ = 11875\]
Thus, the modal income is ₹11875.
APPEARS IN
RELATED QUESTIONS
Describe some fundamental characteristics of statistics.
Explain the meaning of the term Variable.
Explain the meaning of the term Class-integral.
Explain the meaning of the term Class limits.
Explain the meaning of the term Frequency.
Find the mean, median and mode of the following data:
| Class | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 | 60 – 70 |
| Frequency | 4 | 4 | 7 | 10 | 12 | 8 | 5 |
Find the mean, median and mode of the following data:
| Marks obtained | 25 - 35 | 35 – 45 | 45 – 55 | 55 – 65 | 65 – 75 | 75 - 85 |
| No. of students | 7 | 31 | 33 | 17 | 11 | 1 |
The following table gives the daily income of 50 workers of a factory:
| Daily income (in Rs) | 100 – 120 | 120 – 140 | 140 – 160 | 160 – 180 | 180 – 200 |
| No. of workers | 12 | 14 | 8 | 6 | 10 |
Find the mean, median and mode of the above data.
The table below shows the daily expenditure on food of 30 households in a locality:
| Daily expenditure (in Rs) | Number of households |
| 100 – 150 | 6 |
| 150 – 200 | 7 |
| 200 – 250 | 12 |
| 250 – 300 | 3 |
| 300 – 350 | 2 |
Find the mean and median daily expenditure on food.
In a class test, 50 students obtained marks as follows:
| Marks obtained | 0 – 20 | 20 – 40 | 40 – 60 | 60 – 80 | 80 – 100 |
| Number of Students | 4 | 6 | 25 | 10 | 5 |
In a class test, 50 students obtained marks as follows:
In a frequency distribution table with 12 classes, the class-width is 2.5 and the lowest class boundary is 8.1, then what is the upper class boundary of the highest class?
In the following data, find the values of p and q. Also, find the median class and modal class.
| Class | Frequency (f) | Cumulative frequency (cf) |
| 100 – 200 | 11 | 11 |
| 200 – 300 | 12 | p |
| 300 – 400 | 10 | 33 |
| 400- 500 | Q | 46 |
| 500 – 600 | 20 | 66 |
| 600 – 700 | 14 | 80 |
The daily income of a sample of 50 employees are tabulated as follows:
| Income (in Rs.): | 1-1200 | 201 -400 | 401-600 | 601 - 800 |
| No.of employees : | 14 | 15 | 14 | 7 |
Find the mean daily income of employees.
Find the class marks of classes 10−25 and 35−55.
Which of the following is not a measure of central tendency?
Explain the meaning of the following terms: Variate
The times, in seconds, taken by 150 athletes to run a 110 m hurdle race are tabulated below:
| Class | 13.8 – 14 | 14 – 14.2 | 14.2 – 14.4 | 14.4 – 14.6 | 14.6 – 14.8 | 14.8 – 15.0 |
| Frequency | 2 | 4 | 5 | 71 | 48 | 20 |
The number of athletes who completed the race in less than 14.6 seconds is:
Can the experimental probability of an event be a negative number? If not, why?
Can the experimental probability of an event be greater than 1? Justify your answer.
The Empirical relation between the three measures of central tendency is ______.
