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Question 1. The marks obtained by 17 students in a mathematics test (out of 100) are given below:
48, 66, 68, 49, 91, 72, 64, 46, 90, 79, 76, 82, 65, 96, 100, 82, 100
Find the range of the data.
Solution: Lowest observation = 46
Highest observation = 100
∴ Range = 100 –46 = 54
Question 2. The classmark of the class 130 – 150 is:
Solution: Classmark = ((130+150)/2)
= (280/2)
= 140
Question 3. The median of the following numbers arranged in descending order is 25. Find the value of
x: 40, 38, 35, 2x + 10, 2x + 1, 15, 11, 8, 5
Solution: Number of observations = 9
∴ The median is the ((n+1)/2)th term i.e. ((9+1)/2) th or the 5^{th} term.
⇒ 2x + 1 = 25
⇒ x= (251)/2= 12
Question 4. If the mean of 6, x, 4, and 12 is 8, then find the value of x.
Solution:
∴ = 8 or 22 + x = 32
or x = 32 – 22 = 10
Question 5. Find the range of the data 9, 7, 5, 7, 9, 9, 6, 18, 9 and 8.
Solution: Highest data = 18
Lowest data = 5
⇒ Range = 18 – 5 = 13
Question 6. Calculate the median of : 152, 155, 160, 144, 145, 148, 147, 149, 150
Solution: Writing the given data in ascending order, we get: 144, 145, 147, 148, 149, 150, 152, 155, 160
Here, n = 9
∴ Median = term = term = 5^{th} term
⇒ Median = 149
Question 7. What is the median of 70, 40, 50, 100, 75, 75, 65 and 95?
Solution: In ascending order, the given data is:
40, 50, 65, 70, 75, 75, 95, 100
Here, n = 8 (Even number)
⇒ Median =
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