Edexcel IAL S1 Data and Summary Statistics Questions
Types of data (qualitative/quantitative, discrete/continuous); mean, median, mode, quartiles and percentiles; variance and standard deviation; coding; outliers. (Sampling methods are not in IAL S1.)
- S1 · Statistics 1
- Calculator allowed
- 70 practice questions
What the questions test
The 70 S1 data and summary statistics practice questions cover:
Worked example 1
Two different groups of students took a memory test.
Group A consists of \(20\) students. Their mean score is \(15\) and the standard deviation is \(3\).
Group B consists of \(30\) students. Their mean score is \(20\) and the standard deviation is \(4\).
The two groups are combined into a single group of \(50\) students.
Find the combined mean score.
By calculating the total sum of squares (\(\sum x^2\)) for each group separately, find the overall standard deviation of the combined group.
Mark scheme
Sum A \(= 20 \times 15 = 300\). Sum B \(= 30 \times 20 = 600\). M1
Total Sum \(= 300 + 600 = 900\). Total students \(= 50\).
Combined mean \(= \frac{900}{50} = 18\). A1For Group A: \(\sigma_A^2 = 3^2 = 9\).
\(9 = \frac{\sum x_A^2}{20} - 15^2 \implies \frac{\sum x_A^2}{20} = 9 + 225 = 234 \implies \sum x_A^2 = 4680\). M1A1
For Group B: \(\sigma_B^2 = 4^2 = 16\).
\(16 = \frac{\sum x_B^2}{30} - 20^2 \implies \frac{\sum x_B^2}{30} = 16 + 400 = 416 \implies \sum x_B^2 = 12480\). M1A1
Total sum of squares \(\sum x^2 = 4680 + 12480 = 17160\). A1
Combined Variance \(= \frac{17160}{50} - 18^2 = 343.2 - 324 = 19.2\). M1
Combined SD \(= \sqrt{19.2} = 4.3817... \implies 4.38\) (3sf). A1
Worked example 2
The mean of three numbers, \(a\), \(b\), and \(c\), is exactly \(8\). The variance of these three numbers is \(10\).
Using the formula for variance, prove that \(a^2 + b^2 + c^2 = 222\).
Given that \(c = 10\), find the mean and the variance of the remaining two numbers, \(a\) and \(b\).
Mark scheme
Let the sum of squares be \(\sum x^2 = a^2 + b^2 + c^2\).
Using the variance formula: \(\text{Var}(X) = \frac{\sum x^2}{n} - \mu^2\). M1
\(10 = \frac{a^2 + b^2 + c^2}{3} - 8^2\). M1
\(10 = \frac{a^2 + b^2 + c^2}{3} - 64 \implies 74 = \frac{a^2 + b^2 + c^2}{3}\). A1
\(a^2 + b^2 + c^2 = 3 \times 74 = 222\). A1 *If \(c = 10\), then \(a + b + 10 = 3 \times 8 = 24 \implies a + b = 14\). M1
New mean for just \(a\) and \(b\): \(\frac{14}{2} = 7\). A1
Substitute \(c=10\) into sum of squares: \(a^2 + b^2 + 100 = 222 \implies a^2 + b^2 = 122\). M1
New Variance for \(a\) and \(b\) \(= \frac{a^2 + b^2}{2} - (\text{New Mean})^2\). M1
\(= \frac{122}{2} - 7^2 = 61 - 49 = 12\). A1
FAQ
What data and summary statistics is in Edexcel IAL S1?
Types of data (qualitative/quantitative, discrete/continuous); mean, median, mode, quartiles and percentiles; variance and standard deviation; coding; outliers. (Sampling methods are not in IAL S1.)
Is S1 a calculator paper?
Yes, a calculator is allowed in S1, but method marks are only given for working you write down.
How are S1 data and summary statistics questions marked?
With M marks for a correct method, A marks for accurate answers that depend on the M mark before them, and B marks for independent results, as in the worked examples on this page.