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QuestionDetermine if the scores 2,3,3,4,92, 3, 3, 4, 9 (mean M=5M = 5) are above or below the median, given n=6n = 6.

Studdy Solution

STEP 1

Assumptions1. The sample consists of n=6n =6 scores. . The scores are ,3,3,4,9,3,3,4,9 and one missing value.
3. The seesaw is balanced (rests level) when it pivots at a point equal to the sample mean M=5M =5.

STEP 2

First, we need to find the missing score. We know that the mean of all scores is5. The mean is calculated by summing all scores and dividing by the number of scores. So, we can set up the following equation to find the missing scoreM=∑i=1nxinM = \frac{\sum_{i=1}^{n}x_i}{n}

STEP 3

Now, plug in the given values for the mean, the known scores, and the number of scores to calculate the missing score.
5=2+3+3++9+x65 = \frac{2 +3 +3 + +9 + x}{6}

STEP 4

olve the equation for xx.
times6=2+3+3+4+9+x \\times6 =2 +3 +3 +4 +9 + x

STEP 5

Calculate the missing score.
30=2+3+3+4+9+x30 =2 +3 +3 +4 +9 + xx=30−2−3−3−4−9=9x =30 -2 -3 -3 -4 -9 =9So, the missing score is9.

STEP 6

Now that we have all the scores, we can find the median. The median is the middle score when all scores are arranged in ascending order. If there is an even number of scores, the median is the average of the two middle scores.
Our scores in ascending order are 2,3,3,4,9,92,3,3,4,9,9.

STEP 7

Since we have an even number of scores, we need to find the average of the two middle scores.
Median=3+42Median = \frac{3 +4}{2}

STEP 8

Calculate the median.
Median=3+42=3.5Median = \frac{3 +4}{2} =3.5

STEP 9

Now that we have the median, we can determine if each score is above or below the median.
Scores2,3, and3 are below the median. Scores4,9, and9 are above the median.

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