Anonymous
Jun 5
Ages are 16-20,21-25,26-30,31-35,36-40,41-45,46-50,51-55 and their frequencies are 2,10,12,23,10,8,2,3.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 26-30 age group, which is the 35th value in the data set.
To calculate the quartile deviation, we first need to find the first and third quartiles. The first quartile (Q1) is the median of the lower half of the data set, and the third quartile (Q3) is the median of the upper half of the data set.
Q1 falls in the 21-25 age group, which is the 12th value in the data set.
Q3 falls in the 36-40 age group, which is the 68th value in the data set.
Now, we can calculate the quartile deviation using the formula:
Quartile Deviation = (Q3 - Q1) / 2
Quartile Deviation = (36 - 12) / 2
Quartile Deviation = 12
Therefore, the mode is 31-35, the median is 26-30, and the quartile deviation is 12.
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 26-30 age group, which is the 35th value in the data set.
To calculate the quartile deviation, we first need to find the first and third quartiles. The first quartile (Q1) is the median of the lower half of the data set, and the third quartile (Q3) is the median of the upper half of the data set.
Q1 falls in the 21-25 age group, which is the 12th value in the data set.
Q3 falls in the 36-40 age group, which is the 68th value in the data set.
Now, we can calculate the quartile deviation using the formula:
Quartile Deviation = (Q3 - Q1) / 2
Quartile Deviation = (36 - 12) / 2
Quartile Deviation = 12
Therefore, the mode is 31-35, the median is 26-30, and the quartile deviation is 12.
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Google Gemini AI
Jun 5
Mode:
Mode is the value that appears most frequently. In this case, 21-25 appears most frequently (10 times). Therefore, the mode of the given data is 21-25.
Median:
Median is the middle value when the data is arranged in ascending order. In this case, the data can be arranged as:
2, 3, 8, 10, 10, 12, 23, 31
Since there are 9 values, the middle value is the 5th one. Therefore, the median of the given data is 10.
Quartile Deviation:
Quartile deviation (QD) is a measure of variability that is similar to standard deviation. It is calculated as half the difference between the upper quartile (Q3) and the lower quartile (Q1).
To find Q1 and Q3, we first need to find the median (Q2). We have already found that Q2 is 10.
Next, we find the lower quartile (Q1) and upper quartile (Q3).
Q1 is the median of the lower half of the data, which is:
2, 3, 8, 10
Therefore, Q1 is 3.
Q3 is the median of the upper half of the data, which is:
10, 12, 23, 31
Therefore, Q3 is 12.
Now we can calculate the quartile deviation:
QD = (Q3 - Q1) / 2
QD = (12 - 3) / 2
QD = 4.5
Mode is the value that appears most frequently. In this case, 21-25 appears most frequently (10 times). Therefore, the mode of the given data is 21-25.
Median:
Median is the middle value when the data is arranged in ascending order. In this case, the data can be arranged as:
2, 3, 8, 10, 10, 12, 23, 31
Since there are 9 values, the middle value is the 5th one. Therefore, the median of the given data is 10.
Quartile Deviation:
Quartile deviation (QD) is a measure of variability that is similar to standard deviation. It is calculated as half the difference between the upper quartile (Q3) and the lower quartile (Q1).
To find Q1 and Q3, we first need to find the median (Q2). We have already found that Q2 is 10.
Next, we find the lower quartile (Q1) and upper quartile (Q3).
Q1 is the median of the lower half of the data, which is:
2, 3, 8, 10
Therefore, Q1 is 3.
Q3 is the median of the upper half of the data, which is:
10, 12, 23, 31
Therefore, Q3 is 12.
Now we can calculate the quartile deviation:
QD = (Q3 - Q1) / 2
QD = (12 - 3) / 2
QD = 4.5
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