Answer:
Explanation:
To find the missing frequencies in the table, we need to calculate the remaining values.
Given:
Mode = 34
Median = ?
Class limits: 0-9, 10-19, 20-29, 30-39, 40-49, 50-59, 60-69
Total frequency: 4, 16, f?, f?, f?, 6, 4
Total = 230
First, let's find the median class. The median is the middle value when the frequencies are cumulatively added up and reach half of the total frequency.
Total frequency = 230
Median class: ???
To find the median class, we calculate the cumulative frequencies by adding up the frequencies starting from the first class interval until the cumulative frequency is greater than or equal to 115 (half of the total frequency).
Cumulative frequency:
0-9: 4
10-19: 20 (4 + 16)
20-29: ??
30-39: ??
40-49: ??
50-59: ??
60-69: 230 (4 + 16 + ?? + ?? + ?? + 6 + 4)
Since the cumulative frequency of 30-39 is greater than or equal to 115 (half of the total frequency), the median class is 30-39.
Now, let's find the median value within the median class.
Median class: 30-39
Median value: ???
To find the median value within the median class, we need to know the cumulative frequency of the class just before the median class, as well as the frequency of the median class.
Cumulative frequency of the class before the median class (20-29): ??
The cumulative frequency of the class before the median class plus the frequency of the median class should be greater than 115. Let's assume the missing cumulative frequency of the class before the median class is represented by "x."
x + ? (frequency of the median class) > 115
Since the total frequency is 230, we can deduce:
230 - 115 = x + ??
So, x = 115 - ??
Now, let's calculate the median value within the median class. Since the median class is 30-39, the median value falls in the range of 30-39.
Median value within the median class: ??
To find the median value within the median class, we can use the formula:
Median value = Lower limit of the median class + (Frequency / 2 - Cumulative frequency before median class) × Class width
In this case, the lower limit of the median class is 30, and the class width is 10.
Median value within the median class = 30 + ((? / 2) - x) × 10
Now we have all the information needed to find the missing frequencies.
Please provide the value for the cumulative frequency of the class before the median class (20-29) so that we can proceed with the calculations.
Answer:
Firstly, let's calculate the missing frequency for the class interval of 30-39.
Given that the mode is 34, it means the class interval with the highest frequency contains the value 34.
From the given table, we can see that the class interval of 30-39 has a frequency of 6.
As the value 34 falls within this interval, we can assume that the frequency of this interval is also the mode, which is 34.
Now, let's calculate the missing frequencies for the class intervals of 40-49 and 50-59.
Given that the median is the middle value of the data, we can find the median class interval by finding the cumulative frequency just greater than half of the total frequency.
Total frequency = 230 Half of the total frequency = 115 Cumulative frequency:
Class interval 0-9: 4
Class interval 10-19: 16 (20)
Class interval 20-29: f? (f?+20)
Class interval 30-39: 34 (f?+20+6)
Class interval 40-49: f? (f?+20+6+34)
Class interval 50-59: f? (f?+20+6+34+f?)
The cumulative frequency just greater than 115 is 126, which falls in the class interval of 40-49.
Therefore, the median class interval is 40-49. To find the median, we can use the formula:
Median = l + ((n/2 - cf) / f) * w where, l = lower class limit of the median class n = total frequency cf = cumulative frequency just less than the median f = frequency of the median class w = width of the median class
Using the values from the table, we can calculate the median as:
Median = 30 + ((115-20) / 34) * 10
Median = 30 + (95/34) * 10
Median = 30 + 27.94
Median ≈ 57.94
As the median falls in the median class interval of 40-49, we can assume that the frequencies of the class intervals of 40-49 and 50-59 are equal. Let's represent the frequency of these class intervals as x.
We know that the total frequency is 230.
Therefore, 4 + 16 + 6 + 34 + x + x + x = 230 58 + 3x = 230 3x = 172 x ≈ 57.33 Rounding off the value of x to the nearest whole number, we get x = 57.
Hence, the missing frequencies are:
Class interval 20-29: 57
Class interval 40-49: 57
Class interval 50-59: 57
