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# Question

# Answer

(a)

If the modal value is 4, n has to be less than 7. So the largest possible value of n is 6.

(b)

When n = 0, the numbers of goals are 1 1 2 2 2 4 **4** 4 4 4 4 4 5. The median is 4.

When n = 1, the numbers of goals are 1 1 2 2 2 3 **4 4** 4 4 4 4 4 5. The median is 4.

When n = 2, the numbers of goals are 1 1 2 2 2 3 3 **4** 4 4 4 4 4 4 5. The median is 4.

When n = 3, the numbers of goals are 1 1 2 2 2 3 3 **3 4** 4 4 4 4 4 4 5. The median is 3.5.

When n = 4, the numbers of goals are 1 1 2 2 2 3 3 3 **3** 4 4 4 4 4 4 4 5. The median is 3.

So the least possible value of n if the median score is 3 is 4.

(c)

The mean is (2 x 1 + 3 x 2 + n x 3 + 7 x 4 + 1 x 5) / (2 + 3 + n + 7 + 1)

= (3n + 41) / (n + 13) = 3 1/9 = 28 / 9

27n + 369 = 28n + 364

n = 5

Hope it helps 🙂

(a)

If the modal value is 4, n has to be less than 7. So the largest possible value of n is 6.

(b)

When n = 0, the numbers of goals are 1 1 2 2 2 4 **4** 4 4 4 4 4 5. The median is 4.

When n = 1, the numbers of goals are 1 1 2 2 2 3 **4 4** 4 4 4 4 4 5. The median is 4.

When n = 2, the numbers of goals are 1 1 2 2 2 3 3 **4** 4 4 4 4 4 4 5. The median is 4.

When n = 3, the numbers of goals are 1 1 2 2 2 3 3 **3 4** 4 4 4 4 4 4 5. The median is 3.5.

When n = 4, the numbers of goals are 1 1 2 2 2 3 3 3 **3** 4 4 4 4 4 4 4 5. The median is 3.

So the least possible value of n if the median score is 3 is 4.

(c)

The mean is (2 x 1 + 3 x 2 + n x 3 + 7 x 4 + 1 x 5) / (2 + 3 + n + 7 + 1)

= (3n + 41) / (n + 13) = 3 1/9 = 28 / 9

27n + 369 = 28n + 364

n = 5

Hope it helps 🙂

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