The given table shows the number of people in different age groups. Find the mean age of the given number of people.Class interval of age (in years) Number of people (f) 25 - 29 10 30 - 34 12 35 - 39 8 40 - 44 5 45 - 49 15 50 - 54 10 55 - 59 15
43.2 years
To find the mean age of the given number of people, we need to calculate the average using the class intervals and their frequencies. The steps to find the mean age using the formula for the mean in grouped data are outlined below:
Step 1: Calculate the Midpoint of Each Class Interval
The midpoint (or class mark) of each class interval is calculated by taking the average of the lower and upper bounds of each class.
- For 25 - 29: \frac{25 + 29}{2} = 27
- For 30 - 34: \frac{30 + 34}{2} = 32
- For 35 - 39: \frac{35 + 39}{2} = 37
- For 40 - 44: \frac{40 + 44}{2} = 42
- For 45 - 49: \frac{45 + 49}{2} = 47
- For 50 - 54: \frac{50 + 54}{2} = 52
- For 55 - 59: \frac{55 + 59}{2} = 57
Step 2: Multiply the Midpoint by the Frequency
- 27 × 10 = 270
- 32 × 12 = 384
- 37 × 8 = 296
- 42 × 5 = 210
- 47 × 15 = 705
- 52 × 10 = 520
- 57 × 15 = 855
Step 3: Calculate the Sum of the Products and the Total Frequency
- Sum of the products = 270 + 384 + 296 + 210 + 705 + 520 + 855 = 3240
- Total frequency (N) = 10 + 12 + 8 + 5 + 15 + 10 + 15 = 75
Step 4: Calculate the Mean
The mean is calculated using the formula:
\text{Mean} = \frac{\sum \left( f \times x \right)}{N} = \frac{3240}{75} = 43.2Therefore, the mean age of the given number of people is 43.2 years.
This calculation confirms that the correct answer is 43.2 years.
Similar Questions
If the marks scored by the students in a class test out of 50 then, Find the Median of the following data:
Marks Frequency 0-10 5 10-20 8 20-30 6 30-40 6 40-50 5 The marks obtained by 9 students in a test are: 5, 8, 7, 9, 6, 7, 8, 7, 10.
Determine: (i) Mode of the marks, (ii) Number of students scoring above average.
If the mode of the data set {a, a + 2, a + 4, a + 6, a + 6, a + 6, a + 8} is 26, find a.
The given table shows the number of people in different age groups. Find the mean age of the given number of people.
Class interval of age (in years) Number of people (f) 25 - 29 10 30 - 34 12 35 - 39 8 40 - 44 5 45 - 49 15 50 - 54 10 55 - 59 15 If the mode of the data set {a, a + 2, a + 4, a + 6, a + 6, a + 6, a + 8} is 26, find a.
If the marks scored by the students in a class test out of 50 then, Find the Median of the following data:
Marks Frequency 0-10 5 10-20 8 20-30 6 30-40 6 40-50 5 The marks obtained by 9 students in a test are: 5, 8, 7, 9, 6, 7, 8, 7, 10. Determine: (i) Mode of the marks, (ii) Number of students scoring above average.
Important Questions from Statistics
The mean and variance of five observations are 14 and 13.2 respectively. Three of the five observations are 11, 16 and 20. What are the other two observations ?
A die is thrown 10 times and obtained the following outputs :
1, 2, 1, 1, 2, 1, 4, 6, 5, 4
What will be the mode of data so obtained ?
Consider the following frequency distribution :
x 1 2 3 5 f 4 6 9 7 What is the value of median of the distribution ?
For data -1, 1, 4, 3, 8, 12, 17, 19, 9, 11; if M is the median of first 5 observations and N is the median of last five observations, then what is the value of 4M - N ?
Let P, Q, R represent mean, median and mode. If for some distribution \(5 P=4 Q=\frac{R}{2}\) then what is \(\frac{P+Q}{2 P+0.7 R}\) equal to ?
