22. The marks obtained by students in a
mathematics test are given below 1, 3, 2, 2,
3, 4, 1, 5, 10, 11, 9, 8, 12, 14. If A is the
mean and B is the median, then calculate A
− B.
A. 1.68
B. 1.57
C. 2.45
D. 3.58
To find the mean (A), we need to calculate the sum of the given numbers and divide it by the total number of values.
Sum of numbers = 1 + 3 + 2 + 2 + 3 + 4 + 1 + 5 + 10 + 11 + 9 + 8 + 12 + 14 = 85
Total number of values = 14
Mean (A) = Sum of numbers/Total number of values = 85/14 ≈ 6.07
To find the median (B), we need to arrange the numbers in ascending order.
1, 1, 2, 2, 3, 3, 4, 5, 8, 9, 10, 11, 12, 14
Since there are 14 numbers, the median will be the average of the 7th and 8th numbers.
Median (B) = (3 + 4)/2 = 7/2 = 3.5
A - B = 6.07 - 3.5 = 2.57
Therefore, the correct answer is B. 1.57
To calculate A - B, we first need to determine the mean (A) and the median (B) of the given set of marks.
To find the mean:
1. Add up all the marks: 1 + 3 + 2 + 2 + 3 + 4 + 1 + 5 + 10 + 11 + 9 + 8 + 12 + 14 = 85.
2. Calculate the total number of marks: 14 (since there are 14 marks given).
3. Divide the sum of all the marks by the total number of marks: 85 ÷ 14 = 6.07 (rounded to two decimal places).
Therefore, the mean (A) is 6.07.
To find the median:
1. Sort the marks in ascending order: 1, 1, 2, 2, 3, 3, 4, 5, 8, 9, 10, 11, 12, 14.
2. The median is the middle number in the sorted list. Since there are 14 marks, the middle two numbers are 8 and 9.
3. Calculate the average of the two middle numbers: (8 + 9) ÷ 2 = 8.5 (rounded to one decimal place).
Therefore, the median (B) is 8.5.
Now we can calculate A - B:
A - B = 6.07 - 8.5 = -2.43 (rounded to two decimal places).
Therefore, the value of A - B is approximately -2.43.