Write down the standard deviation of the data.
About this question
Question 1.2 of Mathematics Grade 12 Paper 2, NSC Examination (May/June) (DBE, May/June 2025). It tests the Term 3 ATP topic Statistics (Regression and Correlation).
- TermTerm 3
- ATP topicStatistics (Regression and Correlation)
- PaperPaper 2
- Marks1 mark
An insurance broker signed contracts with 15 people. The monthly premium (in rands) payable on each contract is:
\(134;\ 215;\ 325;\ 326;\ 362;\ 429;\ 515;\ 531;\ 598;\ 610;\ 624;\ 728;\ 923;\ 1\,034;\ 1\,200\)
Use the calculator in STAT mode (population standard deviation \(\sigma\)).
\(\sigma = 291{,}03\)
More Questions On Statistics (Regression and Correlation)
Use the calculator in linear regression (STAT, \(A + Bx\)) mode with the 10 data pairs.
\[a = -43{,}72\]\[b = 2{,}36\]\(\hat{y} = -43{,}72 + 2{,}36x\)
About \(22{,}35\) push-ups (so about 22 push-ups)
Find the frequency of each class by subtracting consecutive cumulative frequencies:
\(0 \lt t \leq 20\): \(16\); \(20 \lt t \leq 40\): \(40 - 16 = 24\); \(40 \lt t \leq 60\): \(59 - 40 = 19\); \(60 \lt t \leq 80\): \(67 - 59 = 8\); \(80 \lt t \leq 100\): \(70 - 67 = 3\)
Draw bars with no gaps: \(x\)-axis Time, \(t\) (minutes) marked 0, 20, 40, 60, 80, 100; \(y\)-axis Number of people.
Bar heights 16, 24, 19, 8, 3 for the five classes, bars touching.
So the 9th player scored 10 points.
Using the calculator on all 9 scores:
\[\sigma = 5{,}23 \ (5{,}2281\ldots)\]\[(\bar{x} - \sigma\,;\,\bar{x} + \sigma) = (12 - 5{,}23\,;\,12 + 5{,}23) = (6{,}77\,;\,17{,}23)\]Scores outside this interval: 2, 19 and 20.
3 players
Ground the curve at \((20\,;\,0)\), the lower boundary of the first class.
Plot each cumulative frequency at the upper boundary of its class: \((30\,;\,8)\), \((40\,;\,22)\), \((50\,;\,38)\), \((60\,;\,59)\), \((70\,;\,75)\), \((80\,;\,84)\), \((90\,;\,90)\), \((100\,;\,92)\).
Join the points with a smooth, increasing S-shaped curve.
Ogive from \((20\,;\,0)\) rising through the plotted points to \((100\,;\,92)\).