Exercise 1 Page 125

Let's rearrange the scores from the least to the greatest first. 4, 5, 6, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 25, 26, 27, 28, 29. Now we can find the median, lower quartile, and upper quartile!

Median

Since there is an even number of values, the mean of the middle two values is the median. Let's find it!

Mean=Sum of values/Number of values

SubstituteValues

Substitute values

Mean=16+17/2

AddTerms

Add terms

Mean=33/2

CalcQuot

Calculate quotient

Mean=16.5

Therefore, the median is 16.5.

Lower Quartile

The lower quartile Q_1 is the median of the lower half. There are 20 scores, so we can identify the lower half by taking the first 10 scores. 4, 5, 6, 9, 10, 11, 12, 14, 15, 16 The median is the mean of the two middle values. Let's find it!

Mean=Sum of values/Number of values

SubstituteValues

Substitute values

Mean=10+11/2

AddTerms

Add terms

Mean=21/2

CalcQuot

Calculate quotient

Mean=10.5

Therefore, the lower quartile is Q_1=10.5.

Upper Quartile

The upper quartile Q_3 is the median of the upper half. The upper half will be the remaining 10 scores. 17, 18, 20, 21, 22, 25, 26, 27, 28, 29 Again, we have to find the mean of the two middle values. Let's do it!

Mean=Sum of values/Number of values

SubstituteValues

Substitute values

Mean=22+25/2

AddTerms

Add terms

Mean=47/2

CalcQuot

Calculate quotient

Mean=23.5

Therefore, the upper quartile is Q_3=23.5.