Question 1
Question: Find the median of : 83, 37, 70, 29, 45, 63, 41, 70, 30, 54
Answer: 29, 30, 37, 41, 45, 54, 63, 70, 70, 83
Median = Middle-most score

Median = 49.5
Question 2
Question: The median of prime numbers between 51 and 80.
Answer: 53, 59, 61, 67, 71, 73, 79
Median = Middle-most score
Median = 67
Question 3
Question: The median of the first ten prime numbers.
Answer: The first 10 prime numbers ={2, 3, 5, 7, 11, 13, 17, 19, 23, 29}


Question 4
Question: The following is in ascending order: 12, 14, 17, 20, 22, x, 26, 28, 32, 36
i) If the median of the data is 23, find x.
ii) In the above data, if 32 is changed to 23, find the new median.
Answer: 12, 14, 17, 20, 22, x, 26, 28, 32, 36
i) Median = 23

46 = 22+x
x = 24
ii) Replacing 32 by 23.
12, 14, 17, 20, 22, 23, 24, 26, 28, 36

Median = 22.5
Question 5
Question: The weights of 10 students (in kg) are:
55, 51, 60, 38, 52, 42, 49, 63, 47, 35
i) Find the median weight.
ii) If the weight 63 kg is replaced by 36 kg, find the new median weight.
Answer: i) 35, 38, 42, 47, 49, 51, 52, 55, 60, 63

Median = 50
ii) If 63 kg is replaced by 36 kg.
35, 36, 38, 42, 47, 49, 51, 52, 55, 60

Median = 48kg
Question 6
Question: The mean of 31 results is 60. If the mean of the first 16 results is 58 and that of the last 16 results is 62, find the 16th result.
Answer: The sum of 31 results = 60 x 31 = 1860
The sum of first 16 results = 58 x 16 = 928
The sum of second 16 results = 62 x 16 = 992
16th result = (928 + 992) - 1860 = 60
16th result = 60
Question 7
Question: Find the mean
for the following distribution:

Answer:


Mean=7.025
Question 8
Question: Find the value of 'p', if the mean of the following distribution is 7.5.

Answer:

Mean=7.5

303 + 9p = 7.5(41 + p)
303 + 9p = 307.5 + 7.5p
9p - 7.5p = 307.5 - 303
1.5p = 4.5

p = 3
Question 9
Question: Find the median of : 15, 8, 14, 20, 13, 12, 16.
Answer: 8, 12, 13, 14, 15, 16, 20
n = 7 (odd)

Median = 14
Question 10
Question: Find the mode of : 43, 42, 44, 40, 48, 45, 40, 40
Answer: 40, 40, 40, 42, 43, 44, 45, 48
Since 40 is the most repeated score,
Mode = 40
