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Graphs and Charts with Worked Examples

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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 16^t^h 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
16^t^h result = (928 + 992) - 1860 = 60
16^t^h result = 60