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Mean, Median and Mode · Question 32 of 67

The weekly pocket money (in ₹) of a group of students is shown below, with one frequency missing.

Question 32

HardOriginal question
Pocket money (₹)Number of students
0–205
20–408
40–60pp
60–8012
80–1007

The weekly pocket money (in ₹) of a group of students is shown below, with one frequency missing. The mean weekly pocket money is ₹54. What is pp?

Options for question 32

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. Class marks: 10, 30, 50, 70, 90.

  2. ∑fx=50+240+50p+840+630=1760+50p\sum fx = 50 + 240 + 50p + 840 + 630 = 1760 + 50p, and ∑f=32+p\sum f = 32 + p.

  3. 1760+50p32+p=54\frac{1760 + 50p}{32 + p} = 54, so 1760+50p=1728+54p1760 + 50p = 1728 + 54p.

  4. 4p=324p = 32, giving p=8p = 8.

Worth noting

32 is 4p, before dividing by 4, and it is also the total of the other frequencies. 40 is the total number of students once p is found, not p itself.

Concept
Missing frequency from a given grouped mean
Typical time
120 s
Your time
—
The rule this testsFrequency tables
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Ten questions from Mean, Median and Mode, at your own pace.

Practise this chapter →

Ten questions from Mean, Median and Mode, at your own pace.