Question 21
Question: Find the Median for the following set of scores:
26, 32, 35, 24, 27, 30, 28, 25, 33, 43.
Answer: 24, 25, 26, 27, 28, 30, 32, 33, 35, 43
n = 10 (even)
Median = 29
Question 22
Question: The Median of the first 10 multiples of five.
Answer: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
Median = Middle-most score
Question 23
Question: Find the Mean and Median of:
133, 73, 89, 108, 94, 140, 94, 85, 100, 120
Answer: 73, 85, 89, 94, 94, 100, 108, 120, 133, 140
(arranged in ascending order)
Mean = 103.6
Median = 97
Question 24
Question: Find the Median for the following data:
46, 64, 87, 41, 58, 77, 35, 90, 55, 33, 92
If in the data above, 92 is replaced by 19, determine the new median.
Answer: 33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92
i) n = 11
Median = 58
ii) If 92 is replaced by 19.
19, 33, 35, 41, 46, 55, 58, 64, 77, 87, 90
Median = 55
Question 25
Question: The average score of boys in an examination of a school is 71 and that of the girls is 73. The average score of the school in the examination is 71.8. Find the ratio of the number of boys to the number of girls.
Answer: Let the number of boys be = x
Let the number of girls be = y
Total score of boys = 71x
Total score of girls = 73y
Total score of all students = 71.8 (x + y)
71.8 (x+y) = 71x + 73y
Therefore the ratio of the number of boys to the number of girls is 3:2.
Question 26
Question: The mean of 20 numbers is 20. If 2 is added to each of the first 10 numbers, find the mean of the new set of 20 numbers.
Answer: Sum of 20 numbers = 20 x 20 = 400
When 2 is added to the first 10 numbers, the new sum =400+20=420
New Mean = 21
Question 27
Question: If the mean of the following distribution is 6, find the value of p.
Answer:
N = 11
Mean = 6
66 = 53 + 2p
2p = 13
p = 6.5
Question 28
Question: Calculate the arithmetic mean of the following frequency distribution:
Answer:
Mean = 141.875
Question 29
Question: Find the Mode of the following marks obtained by 16 students in a subject:
0, 0, 2, 2, 3, 3, 4, 5, 5, 5, 5, 6, 6, 7, 8
Answer: Since 5 is the most repeated score,
Mode = 5
Question 30
Question: The marks obtained by 102 students in a physics test is given below. Find the average marks.
Answer:
Mean = 26.08
