MathAmigo

Statistical Data Analysis

Secondary 4 practice

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Statistical Data Analysis practice questions

Secondary 4 topics from the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

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What this topic covers

Worked examples

Example 1

The cumulative frequency table below shows the average amount of time that adults exercise daily. There are 60 observations in total. Find the percentage of adults who exercise for at least 2020 minutes a day.
Cumulative frequency (x)Number of observations
x < 100
x < 206
x < 3018
x < 4036
x < 5050
x < 6057
x < 7060
Show the worked solution
  • Number with x<20=6read from table\text{Number with } x < 20 = 6 \quad \scriptsize\textit{read from table}
  • Number with x≥20=60−6\text{Number with } x \geq 20 = 60 - 6
  • =54= 54
  • Percentage=5460×100%\text{Percentage} = \dfrac{54}{60} \times 100\%
  • =90%= 90\%

Answer: 9090

Example 2

The following data shows the masses, in kg, of some parcels. 15, 18, 20, 21, 23, 24, 25, 26, 27, 28, 31, 32, 35, 36, 38, 3915,\ 18,\ 20,\ 21,\ 23,\ 24,\ 25,\ 26,\ 27,\ 28,\ 31,\ 32,\ 35,\ 36,\ 38,\ 39 Find the interquartile range (IQR).
Show the worked solution
  • Arrange the data in ascending order:
  • 15, 18, 20, 21, 23, 24, 25, 26, 27, 28, 31, 32, 35, 36, 38, 3915,\ 18,\ 20,\ 21,\ 23,\ 24,\ 25,\ 26,\ 27,\ 28,\ 31,\ 32,\ 35,\ 36,\ 38,\ 39
  • Number of values: n=16n = 16 (even)
  • Q2=26+272mean of 8th and 9th valuesQ_2 = \dfrac{26 + 27}{2} \quad \scriptsize\textit{mean of 8th and 9th values}
  • =532= \dfrac{53}{2}
  • =26.5= 26.5
  • Lower half: 15, 18, 20, 21, 23, 24, 25, 2615,\ 18,\ 20,\ 21,\ 23,\ 24,\ 25,\ 26
  • Q1=21+232Q_1 = \dfrac{21 + 23}{2}

Answer: 11.511.5

Example 3

The cumulative frequency table shows the times, in hours, that pupils spent on a computer in a week, for 160160 observations. Estimate the 4040th percentile, P40P_{40}.
Time (x ≤)610141822
Cumulative frequency16324864160
Show the worked solution
  • The position of P40P_{40} is 40100×160\dfrac{40}{100} \times 160
  • =64= 64
  • Reading the value with a cumulative frequency of 6464:
  • P40=18P_{40} = 18 hours

Answer: 1818

Questions parents ask

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Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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