The number of match sticks contained in 50 match boxes is given below :
Number of
| 40 | 42 | 43 | 44 | 45 |
Match sticks
Number of boxes 6 | 7 | 2 | 9 | 10 | 6
(i) Using short cut method, find the mean number of match sticks per box.
(ii) How many extra match sticks are to be added to all the contents of 50 match boxes to
bring the mean exactly equal to 45 match sticks per box?
Answers
Concept-
Use the concept of median to find the mean number of match sticks per box and number of extra match sticks to be added.
Given-
Number of match sticks 40 42 43 44 45 48
Number of boxes 6 7 2 9 10 6
Find-
(i) number of mean number of match sticks per box.
(ii) extra match sticks to be added to all the contents of 50 match boxes to bring the mean exactly equal to 45 match sticks per box.
Solution-
Here, A= 44,
Number of match sticks( xi) Number of boxes(fi) di=xi-A fidi
. 40 6 -4 -24
42 7 -2 -14
43 12 -1 -12
44=A 9 0 0
45 10 1 10
48 6 4 -24
TOTAL Σfi=50 Σfidi= -16
(i) ∴Mean=A+ (Σfidi/Σfi)
⇒44+(-16/50)
⇒44-0.32
⇒43.68
Hence, mean number of match sticks per box is 43.68.
(ii) Extra match sticks to have all the contents of 50 match boxes -
⇒ (45-43.68)×50
⇒ 1.32×50
⇒ 66
Hence, extra match sticks to have all the contents of 50 match boxes is 66.
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