90+ marks in Unit 12 – short solutions!
HSA Notes Features
- 100% NBF/FBISE correct
- Ex 12.1–12.4 + Misc solved
- Quick revision format
- Ogives, dispersion, correlation
- Free PDF with graphs
- Trusted for high scores
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FBISE + Punjab boards. Top schools: Beaconhouse, Roots, LGS, City School, Karachi Grammar, Aitchison, Lawrence, ICG, APS, FPS.
Unit 12 Key Solved Highlights
Ex 12.1
Q1(i) Total = 30
Q1(ii) 8th item → 21–30
Q1(iii) <21 → 7
Q1(iv) Highest → 31–40 (9)
Q1(v) Lower boundary last = 51
Q2 Weight 4.5 months = 13 kg
Q3 Q1 ≈27.23 yr, D7 ≈37.25 yr, P60 =34.5 yr
Q4 Boys appeared =90, median ≈72.17, below median ≈45, D1=9, P30=27, excellence=2
Q5 Cubs >77 kg =23
Q6 <50 m ≈50, >40 m 72%, ratio 1:1, Q1=25, D8 max ≈62 m, P30 max ≈80 m
Q7 Range Rs.125000, IQR Rs.40000
Q8 75th percentile → outperformed 75%
Q9 Q3 Rs.30M, IQR Rs.10M
Q10 Median ≈40, Q1≈30, Q3≈58, IQR=28, D7≈52, P30≈32
Ex 12.2
Q1 Mass: min1100 Q1 1200 med1500 Q3 1700 max2000
Fuel: min10 Q1 12 med14 Q3 20 max24
IQR mass500 kg, fuel8 km/l → negative correlation, heavier = less efficient
Q2 Full-time median ≈Rs.850
Part-time min100 max800
IQR both Rs.300
No correlation (univariate)
Q3 Positive correlation
Q4 Positive correlation
Q5 Strong positive correlation
Q6 25% above Q3
Ex 12.3
Q1 Dispersion measures spread; range=max-min; variance=∑(x-¯x)²/(n-1); SD=√variance
Q2 Mean500.5 units, range599, variance≈39091
Q3 Mean800.5 gal, variance≈36364, SD≈190.7, CV≈23.8%
Q4 Mean Rs.68667, range Rs.60000, SD≈Rs.15402, CV≈22.4%
Q5 Mean≈66.35, variance≈57.41, SD≈7.58
Q6 Mean Rs.867, range Rs.2000, SD≈Rs.492
Q7 OT mean≈126.5, OPD≈130.8; CV OT≈11%, OPD≈10%
Q8 Jhelum mean≈103.5°F low variance; Indiana≈67.5°F high variance → Indiana harder to forecast
Ex 12.4
Q1 Even product =4/9
Q2 Three tails =1/8
Q3 Either like =17/20
Q4 Either positive =0.58
Q5 Either job =0.7
Q6 Either bus =2/3
Q7 Either win =173/243
Q8 Either defect =0.28
Q9 Both positive =0.63
Q10 Both pass =0.72
Misc Ex 12
i (d) arithmetic mean
ii (b) 2
iii (b) range
iv (c) C.V.
v (d) 0
vi (d) 0
vii (b) quartile
viii (a) decile
ix (d) median
x (c) percentile
xi (c) y=mx+c
xii (a) (SD/mean)×100
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