Statistics Model Questions Set 1 Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (b)

Categorical data

Answer: (b)

Mean = (sum of ∞) / (sum of f) = (5*5 + 12*15 + 10*25 + p*35 + 9*45) / (8 + 12 + 10 + P + 9) = 25.2 (875 + 35P) / (39 + P) = 25.2 ⇒ P = 11

Answer: (c)

Rs.25 = 1 $cm^2$

∴ Rs.1 = $1/{25} cm^2$

∴ Rs.81 = ${81}/{25} cm^2$ = Area of square

Side of square = $√{{81}/{25}} = 9/5$ = 1.8 cm

Answer: (b)

Four slices 150°, 90°, 60°, 60°

when 60° is deleted

Remaining 150°, 90°, 60°

Total = 300°

While making Pie chart where 300° is taken as 100%

${150}/{300}$ × 100 = 50%

${90°}/{300}$ × 100 = 30%

${60°}/{300}$ × 100 = 20%

50% of 360° will be 180°

∴ largest slice as angle – 180°

Answer: (d)

a < b < c

Total numbers = 6

Increasing order a, a, b, b, c, c

∴ Median = ${\text"(6/2)th term + (6/2 + 1)th term"}/2$

= ${\text"3rd term + 4th term"}/2$

2 = ${b + b}/2$ = b

Arithmetic mean = ${a + a + b + b + c + c}/6$

⇒ $7/3 = {a + b + c}/3$

⇒ a + b + c = 7

⇒ a + c = 7 – 2 = 5 ... (i)

Geometric mean = $(a^2 × b^2 × c^2)^{1/6}$

⇒ 2 = $(abc)^{1/3}$

⇒ abc = 8

⇒ ac = $8/2$ = 4 ... (ii)

⇒ c = $4/a$

From equation (i),

a + $4/a$ = 5

⇒ ${a^2 + 4}/a$ = 5

⇒ $a^2$ – 5a + 4 = 0

⇒ $a^2$ – 4a – a + 4 = 0

⇒ a(a – 4) – 1(a – 4) = 0

⇒ (a – 4) (a – 1) = 0

if a = 1 then c = 4

a = 4 then c = 1

a = 1, c = 4 and b = 2

Mode = 3 (Median) – 2 (Mean)

= $3(2) - 2(7/3) = {18 - 14}/3 = 4/3$