Question

Shahruk plays four games of golf. His four scores have a mean of 75, a mode of 78 and a median of 77. Work out his four scores.​

Answer 1

The four scores are 68, 77, 78, and 78.

Step-by-step explanation:

Given:

The mean of the four scores is 75.

So, the sum of all the four scores is equal to the product of mean and number of scores. Therefore,

Sum of scores , 'S' = Mean $\times$ Number of scores.

$S=75\times 4=300----1$

Now, let one of the middle scores be 'x'.

Since the number of scores is even, the median is half of the sum of the two middle terms.

Median is given as 77 and mode is 78.

So, median is given as:

$Median=\frac{x+Mode}{2}\\77=\frac{x+78}{2}\\x+78=77\times 2\\x+78=154\\x=154-78=76$

As 76 is smaller than 78.

So, the 2nd score is 76 and third score is 78.

Since mode is 78, it has to be repeated more than once. So, the fourth score will also be 78.

Now, let the first score be 'y'. Therefore, the sum is given as:

$S=y+76+78+78\\300=y+232\\y=300-232=68$

Therefore, the four scores are 68, 76, 78, and 78.

Answer 2

The four scores are 68, 77, 78, and 78.

Step-by-step explanation:

Given:

The mean of the four scores is 75.

So, the sum of all the four scores is equal to the product of mean and number of scores. Therefore,

Sum of scores , 'S' = Mean  Number of scores.

Now, let one of the middle scores be 'x'.

Since the number of scores is even, the median is half of the sum of the two middle terms.

Median is given as 77 and mode is 78.

So, median is given as:

As 76 is smaller than 78.

So, the 2nd score is 76 and third score is 78.

Since mode is 78, it has to be repeated more than once. So, the fourth score will also be 78.

Now, let the first score be 'y'. Therefore, the sum is given as:

Therefore, the four scores are 68, 76, 78, and 78.