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The number of problems worked out by a student on seven days of a week are 5, 9, 15, 11, 13, 17, 7, then what is the sum of lower quartile and upper quartile?
- a)15
- b)18
- c)22
- d)19
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The number of problems worked out by a student on seven days of a week...
The given data in ascending order is 5, 7, 9, 11, 13, 15, 17
n = 7 (odd)
n = 7 (odd)
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The number of problems worked out by a student on seven days of a week...
To find the sum of the lower quartile and upper quartile, we first need to arrange the given data in ascending order.
The given data is: 5, 9, 15, 11, 13, 17, 7
Arranging the data in ascending order: 5, 7, 9, 11, 13, 15, 17
Finding the Quartiles:
Quartiles divide the data into four equal parts. The lower quartile (Q1) is the median of the lower half of the data, and the upper quartile (Q3) is the median of the upper half of the data.
Step 1: Find the Median (Q2)
Since there are 7 data points, the median will be the 4th value. In this case, the median (Q2) is 11.
Step 2: Find the Lower Quartile (Q1)
The lower quartile (Q1) is the median of the lower half of the data. In this case, the lower half of the data is 5, 7, and 9. Since there are 3 data points, the median will be the 2nd value, which is 7.
Step 3: Find the Upper Quartile (Q3)
The upper quartile (Q3) is the median of the upper half of the data. In this case, the upper half of the data is 13, 15, and 17. Since there are 3 data points, the median will be the 2nd value, which is 15.
Calculating the sum of the lower quartile and upper quartile:
Q1 + Q3 = 7 + 15 = 22
Therefore, the sum of the lower quartile and upper quartile is 22.
Hence, the correct answer is option C) 22.
The given data is: 5, 9, 15, 11, 13, 17, 7
Arranging the data in ascending order: 5, 7, 9, 11, 13, 15, 17
Finding the Quartiles:
Quartiles divide the data into four equal parts. The lower quartile (Q1) is the median of the lower half of the data, and the upper quartile (Q3) is the median of the upper half of the data.
Step 1: Find the Median (Q2)
Since there are 7 data points, the median will be the 4th value. In this case, the median (Q2) is 11.
Step 2: Find the Lower Quartile (Q1)
The lower quartile (Q1) is the median of the lower half of the data. In this case, the lower half of the data is 5, 7, and 9. Since there are 3 data points, the median will be the 2nd value, which is 7.
Step 3: Find the Upper Quartile (Q3)
The upper quartile (Q3) is the median of the upper half of the data. In this case, the upper half of the data is 13, 15, and 17. Since there are 3 data points, the median will be the 2nd value, which is 15.
Calculating the sum of the lower quartile and upper quartile:
Q1 + Q3 = 7 + 15 = 22
Therefore, the sum of the lower quartile and upper quartile is 22.
Hence, the correct answer is option C) 22.
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