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A consumer finds that five bags of popcorn contain 257, 261, 273, 280, 01 Apr 2020, 10:18
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C
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Question Stats:

92% (01:26) correct 8% (01:30) wrong based on 146 sessions

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A consumer finds that five bags of popcorn contain 257, 261, 273, 280, and 259 corn kernels per bag, respectively. What is the average number of corn kernels per bag of popcorn?
A) 246
B) 250
C) 266
D) 276
E) 280
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C
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TestPrepUnlimited
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A consumer finds that five bags of popcorn contain 257, 261, 273, 280, 01 Apr 2020, 13:48
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A consumer finds that five bags of popcorn contain 257, 261, 273, 280, and 259 corn kernels per bag, respectively. What is the average number of corn kernels per bag of popcorn?
A) 246
B) 250
C) 266
D) 276
E) 280
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Instead of adding 5 numbers directly, we can find a nice reference for these 5 numbers. Subtract 257 from all numbers, the set is now:
0, +4, +16, +23, +2. The average of that is (45)/5 = 9. Then we know the average is 9 above 257, so the average is 257 + 9 = 266.

Ans: C.
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A consumer finds that five bags of popcorn contain 257, 261, 273, 280, 01 Apr 2020, 13:40
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Asad
A consumer finds that five bags of popcorn contain 257, 261, 273, 280, and 259 corn kernels per bag, respectively. What is the average number of corn kernels per bag of popcorn?
A) 246
B) 250
C) 266
D) 276
E) 280
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Method 1:
Mean = \(\frac{(257 + 259 + 261 + 273 + 280)}{5} = 266\)

Method 2: Assumed mean method
Assume the mean = \(261\)

—> Actual Mean = \(261 + \frac{(- 4 - 2 + 0 + 12 + 19)}{5}\)
= \(261 + \frac{25}{5}\)
= \(261 + 5\)
= \(266\)

Option C

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A consumer finds that five bags of popcorn contain 257, 261, 273, 280, 29 Apr 2020, 22:50
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TestPrepUnlimited
Asad
A consumer finds that five bags of popcorn contain 257, 261, 273, 280, and 259 corn kernels per bag, respectively. What is the average number of corn kernels per bag of popcorn?
A) 246
B) 250
C) 266
D) 276
E) 280

Instead of adding 5 numbers directly, we can find a nice reference for these 5 numbers. Subtract 257 from all numbers, the set is now:
0, +4, +16, +23, +2. The average of that is (45)/5 = 9. Then we know the average is 9 above 257, so the average is 257 + 9 = 266.

Ans: C.
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TestPrepUnlimited,
Could you generalise above solution ?
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A consumer finds that five bags of popcorn contain 257, 261, 273, 280, 29 Apr 2020, 23:01
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ammuseeru
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Asad
A consumer finds that five bags of popcorn contain 257, 261, 273, 280, and 259 corn kernels per bag, respectively. What is the average number of corn kernels per bag of popcorn?
A) 246
B) 250
C) 266
D) 276
E) 280

Instead of adding 5 numbers directly, we can find a nice reference for these 5 numbers. Subtract 257 from all numbers, the set is now:
0, +4, +16, +23, +2. The average of that is (45)/5 = 9. Then we know the average is 9 above 257, so the average is 257 + 9 = 266.

Ans: C.


TestPrepUnlimited,
Could you generalise above solution ?
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ammuseeru

Yes the above explanation given by testprepunlimited can be generalised.

The only amendment that I would make it that choose the base which is easy such as 260 or 265 rather than choosing 257. It helps in ease of calculation
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A consumer finds that five bags of popcorn contain 257, 261, 273, 280, 06 May 2020, 10:23
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ammuseeru absolutely!

The general idea is, what happens if you subtract 100 from every number in the set? Then the average goes down by 100.
What happens if you multiply every number in the set by 100? Then the average is also multiplied by 100.

When we are trying to find the average, we have multiple ways of manipulating numbers to find an easier "new average" first, then work our way back to the original average. Now try to look at the original explanation again and you might see some intuition in why we are subtracting 257, it makes everything so much easier.

ammuseeru
TestPrepUnlimited
Asad
A consumer finds that five bags of popcorn contain 257, 261, 273, 280, and 259 corn kernels per bag, respectively. What is the average number of corn kernels per bag of popcorn?
A) 246
B) 250
C) 266
D) 276
E) 280

Instead of adding 5 numbers directly, we can find a nice reference for these 5 numbers. Subtract 257 from all numbers, the set is now:
0, +4, +16, +23, +2. The average of that is (45)/5 = 9. Then we know the average is 9 above 257, so the average is 257 + 9 = 266.

Ans: C.


TestPrepUnlimited,
Could you generalise above solution ?
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A consumer finds that five bags of popcorn contain 257, 261, 273, 280, 05 Nov 2023, 20:59
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