Mean deviation about mean is 7.6 and median is 18 for 4,10,x,y,27 then mean is
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Answer:
3 median = mode + mean
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Given :- Let the data 4, 10, x, y, 27 be in increasing order. If the median of data is 18 and its mean deviation about mean is 7.6, then the mean of this data is :-
a) 7
b) 16
c) 16.5
d) 15.5
Solution :-
we know that,
- Median = (n + 1)/2 th term when data is increasing order where n = odd number.
- Mean deviation about mean = ⅀|xi - mean| / No. of observation .
- Mean = (sum of observation) / (Total number of observation.)
we have,
→ 4 < 10 < x < y < 27 = 5 terms.
so,
→ Median = (5 + 1)/2 = 6/2 = 3rd term => x .
therefore, x is equal to 18.
Now, Let us assume that, Mean of this data is z.
so,
→ z = (sum of observation) / (Total number of observation.)
→ z = (4 + 10 + 18 + y + 27)/5
→ z = (59 + y)/5 ------------- Eqn.(1)
Also, we have given that,
→ Mean deviation about mean = 7.6
putting values we get,
→ 7.6 = ⅀|xi - mean| / 5
→ 38 = |4 - z| + |10 - z| + |18 - z| + |y - z| + |27 - z|
since, mean is average of given numbers . it must be near to 18 .
conclusion :-
- |4 - z| = Negative.
- |10 - z| = Negative.
- |18 - z| = Positive
- |y - z| = Positive.
- |27 - z| = Positive.
therefore,
→ 38 = -(4 - z) - (10 - z) + (18 - z) + (y - z) + (27 - z)
→ 38 = (z - 4) + (z - 10) + (18 - z) + (y - z) + (27 - z)
→ 38 = z + z - z - z - z + 18 + y + 27 - 4 - 10
→ 38 = 45 - 14 + y - z
→ 38 = 31 + y - z
→ 38 - 31 = y - z
→ 7 = y - z
→ z = (y - 7) ---------------- Eqn.(2)
comparing Eqn.(1) & Eqn.(2) ,
→ (59 + y) / 5 = (y - 7)
→ 59 + y = 5(y - 7)
→ 59 + y = 5y - 35
→ 59 + 35 = 5y - y
→ 4y = 94
→ y = 23.5
hence,
→ z = (y - 7)
→ z = 23.5 - 7
→ z = 16.5 (C) (Ans.)
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