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Statistics — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsStatistics5 Marks
Question
Marks obtained by 40 students in a short assessment is given below, where a and b are two missing data.
Marks56789
Number of Students6a1613b
If the mean of the distribution is 7.2, find a and b.
✓

Answer

Marks (x)Number of students (f)fx
5630
6a6a
716112
813104
9b9b
`sumf = 34 + a + b``sumfx = 246 + 6a + 9b`
It is given that the number of students is 40.
∴ 35 + a + b = 40
⇒ a + b – 5 = 0      ....(1)
"Mean" = (sum fx)/(sum f)
=> (246 + 6a + 9b)/(35 + a + b) = 7.2`
=> 246 + 6a + 9b = 7.2(35 + a + b)`
=> 246 + 6a + 9b = 252 + 7.2a  + 7.2b`
=> 0 = 252 - 246 + 7.2a - 6a + 7.2b - 9b`
=> 6 + 1.2a - 1.8b = 0`
=> 10 + 2a - 3b = 0`    .... (2)
Solving equations (1) and (2), we have
5a - 5 = 0
=> a = 1
From (1), we have b = 4
Hence, the values of a and b are 1 and 4 respectively.

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