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Mean, Median and Mode · Question 34 of 67

The table shows the lengths of 50 leaves collected on a nature walk, with two frequencies x and y missing.

Question 34

HardOriginal question
Length (mm)Number of leaves
0–106
10–20xx
20–3018
30–4012
40–50yy

The table shows the lengths of 50 leaves collected on a nature walk, with two frequencies xx and yy missing. The median length is 25 mm. What is xx?

Options for question 34

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. Total: 6+x+18+12+y=506 + x + 18 + 12 + y = 50, so x+y=14x + y = 14.

  2. n÷2=25n \div 2 = 25 falls in 20–30, with cf before it =6+x= 6 + x, f=18f = 18, h=10h = 10.

  3. 25=20+25−(6+x)18×1025 = 20 + \frac{25 - (6 + x)}{18} \times 10, so 19−x18×10=5\frac{19 - x}{18} \times 10 = 5.

  4. 19−x=919 - x = 9, giving x=10x = 10 (and y=4y = 4).

Worth noting

9 is the value of 19−x19 - x, one step before the answer. 4 is y, and 16 is the cumulative frequency 6+x6 + x before the median class.

Concept
Missing frequencies from a given grouped median
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.