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Question
In a frequency distribution, the mid-value of a class is 10 and the width of the class is 6. The lower limit of the class is ______.
Options
6
7
8
12
Solution
In a frequency distribution, the mid-value of a class is 10 and the width of the class is 6. The lower limit of the class is 7.
Explanation:
Given: Mid-value = 10
Range = 6
Let upper class and lower class of the interval are x and y respectively.
Now, Mid-value = `("Upper class" + "Lower class")/2`
`10 = (x + y)/2`
x + y = 20 ...(I)
As, Range = Maximum value of data set – Minimum value of data set
6 = x – y
x – y = 6 ...(II)
Adding equation (I) and (II), we get
x + y = (x – y) + 20 + 6
2x = 26
`x = 26/2`
x = 13
Putting the value of x in equation (I), we get
13 + y = 20
y = 20 – 13
y = 7
Hence, the lower limit of the class is 7.
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