Question

If the median of a series exceeds the mean by 3,find by what the number the mode exceeds its mean?​

Answer 1

Step-by-step explanation:

Solution:

PLAN To find the foot of perpendiculars and find its locus.

Formula used

Foot of perpendicular from (x1,y1,z1) to

ax+by+cz+d=0be(x2,y2,z2) then

x2−x1a=y2−y1b=z2−z1c

=−(ax1+by1+cz1+d)a2+b2+c2

Any point on x+22=y+1−1=z3=λ

⇒ x=2λ−2,y=−λ−1,z=3λ

Let foot of perpendicular from (2λ−2,−λ−1,3λ)

to x+ y + z = 3 be (x2,y2,z2).

∴ x2−(2λ−2)1=y2−(−λ−1)1=z2−(3λ)1

=(2λ−2−λ−1+3λ−3)1+1+1

⇒x2−2λ+2=y2+λ+1=z2−3λ=2−4λ3

∴ x2=2λ3,y2=1−7λ3,+2=z2=2+5λ3

⇒ λ=x2−02/3,=1−y2−1−7/3,=+z2−25/3

Hence, foot of perpendicular lie on

=x2/3=y−1−7/3=z−25/3⇒x2=y−1−7=z−25

Answer 2

• let mean = x
• let mean = xthen mode = x+12
• let mean = xthen mode = x+12now, 3 median = mode + 2 mean
• let mean = xthen mode = x+12now, 3 median = mode + 2 mean⇒ 3 median = x + 12 + 2x
• let mean = xthen mode = x+12now, 3 median = mode + 2 mean⇒ 3 median = x + 12 + 2x⇒ 3 median = 3x + 12
• let mean = xthen mode = x+12now, 3 median = mode + 2 mean⇒ 3 median = x + 12 + 2x⇒ 3 median = 3x + 12⇒ 3 median = 3(x + 4)
• let mean = xthen mode = x+12now, 3 median = mode + 2 mean⇒ 3 median = x + 12 + 2x⇒ 3 median = 3x + 12⇒ 3 median = 3(x + 4)⇒ median = x + 4
• let mean = xthen mode = x+12now, 3 median = mode + 2 mean⇒ 3 median = x + 12 + 2x⇒ 3 median = 3x + 12⇒ 3 median = 3(x + 4)⇒ median = x + 4now mode - median = (x + 12) - (x + 4)
• let mean = xthen mode = x+12now, 3 median = mode + 2 mean⇒ 3 median = x + 12 + 2x⇒ 3 median = 3x + 12⇒ 3 median = 3(x + 4)⇒ median = x + 4now mode - median = (x + 12) - (x + 4)so mode - median = x + 12 - x - 4
• let mean = xthen mode = x+12now, 3 median = mode + 2 mean⇒ 3 median = x + 12 + 2x⇒ 3 median = 3x + 12⇒ 3 median = 3(x + 4)⇒ median = x + 4now mode - median = (x + 12) - (x + 4)so mode - median = x + 12 - x - 4⇒ mode - median = 8
• let mean = xthen mode = x+12now, 3 median = mode + 2 mean⇒ 3 median = x + 12 + 2x⇒ 3 median = 3x + 12⇒ 3 median = 3(x + 4)⇒ median = x + 4now mode - median = (x + 12) - (x + 4)so mode - median = x + 12 - x - 4⇒ mode - median = 8Hence mode exceeds median by 8
• Please mark it as brainliest.