Anonymous
Jun 5
Ages are 16-20,21-25,26-30,31-35,36-40,41-45,46-50 and 51-55.their frequencies are 2,10,12,23,10,18,2 and 3.calculate mode, medium and quartile deviation of the above data?
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ChatGPT
Jun 5
To calculate the mode, we need to find the age group with the highest frequency. In this case, the age group with the highest frequency is 31-35 with a frequency of 23.
To calculate the median, we need to find the middle value of the data set. Since the data is already sorted, the median falls in the 4th quartile (26-30). The median age group is 26-30.
To calculate the quartile deviation, we first need to find the first and third quartiles.
First Quartile (Q1):
N = 80 (sum of all frequencies)
Q1 = (N+1)/4 = (80+1)/4 = 20.25
Q1 falls in the 2nd quartile (21-25) with a frequency of 10.
Third Quartile (Q3):
Q3 = 3(N+1)/4 = 3(80+1)/4 = 60.75
Q3 falls in the 5th quartile (36-40) with a frequency of 10.
Now, we can calculate the quartile deviation:
QD = (Q3 - Q1)/2 = (60.75 - 20.25)/2 = 40.5/2 = 20.25
Therefore, the mode is 31-35, the median is 26-30, and the quartile deviation is 20.25.
To calculate the median, we need to find the middle value of the data set. Since the data is already sorted, the median falls in the 4th quartile (26-30). The median age group is 26-30.
To calculate the quartile deviation, we first need to find the first and third quartiles.
First Quartile (Q1):
N = 80 (sum of all frequencies)
Q1 = (N+1)/4 = (80+1)/4 = 20.25
Q1 falls in the 2nd quartile (21-25) with a frequency of 10.
Third Quartile (Q3):
Q3 = 3(N+1)/4 = 3(80+1)/4 = 60.75
Q3 falls in the 5th quartile (36-40) with a frequency of 10.
Now, we can calculate the quartile deviation:
QD = (Q3 - Q1)/2 = (60.75 - 20.25)/2 = 40.5/2 = 20.25
Therefore, the mode is 31-35, the median is 26-30, and the quartile deviation is 20.25.
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Google Gemini AI
Jun 5
1. Mode
Mode is the value that appears most frequently in a dataset. In this case, the value 23 appears most frequently (once). Therefore, the mode of the given data is 23.
2. Median
Median is the middle value of a dataset when arranged in ascending order. To calculate the median, we can first arrange the data in ascending order:
2, 2, 3, 10, 10, 12, 18, 23
Since there are 8 values in the dataset, the median is the average of the 4th and 5th values. Therefore, the median is (10 + 12) / 2 = 11.
3. Quartile Deviation
Quartile deviation is a measure of the variability of a dataset. It is calculated as half of the difference between the upper quartile (Q3) and the lower quartile (Q1). To calculate Q1 and Q3, we first need to find the median (Q2).
As we found earlier, the median (Q2) is 11.
To find Q1, we take the median of the lower half of the dataset (2, 2, 3, 10, 10):
Q1 = (2 + 3) / 2 = 2.5
To find Q3, we take the median of the upper half of the dataset (12, 18, 23):
Q3 = (12 + 18) / 2 = 15
Therefore, the quartile deviation is:
QD = (Q3 - Q1) / 2 = (15 - 2.5) / 2 = 6.25
Mode is the value that appears most frequently in a dataset. In this case, the value 23 appears most frequently (once). Therefore, the mode of the given data is 23.
2. Median
Median is the middle value of a dataset when arranged in ascending order. To calculate the median, we can first arrange the data in ascending order:
2, 2, 3, 10, 10, 12, 18, 23
Since there are 8 values in the dataset, the median is the average of the 4th and 5th values. Therefore, the median is (10 + 12) / 2 = 11.
3. Quartile Deviation
Quartile deviation is a measure of the variability of a dataset. It is calculated as half of the difference between the upper quartile (Q3) and the lower quartile (Q1). To calculate Q1 and Q3, we first need to find the median (Q2).
As we found earlier, the median (Q2) is 11.
To find Q1, we take the median of the lower half of the dataset (2, 2, 3, 10, 10):
Q1 = (2 + 3) / 2 = 2.5
To find Q3, we take the median of the upper half of the dataset (12, 18, 23):
Q3 = (12 + 18) / 2 = 15
Therefore, the quartile deviation is:
QD = (Q3 - Q1) / 2 = (15 - 2.5) / 2 = 6.25
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