Question

jackson collects data on the price of a quart of milk at 8 different stores. the data are listed in order from least to greatest. median = $ 1.75 $1.59 $1.60 $1.64 $1.70 $1.80 $1.83 $1.85 $2.00 find the lower quartile and upper quartile of the data set. lower quartile (q1) = $ upper quartile (q3) = $

Explanation:

Step1: Split the data set

The data set is \( \$1.59, \$1.60, \$1.64, \$1.70, \$1.80, \$1.83, \$1.85, \$2.00 \). Since \( n = 8 \) (even number of data points), the median is the average of the \( 4^{th} \) and \( 5^{th} \) values. To find \( Q1 \) (lower quartile), consider the first half of the data: \( \$1.59, \$1.60, \$1.64, \$1.70 \). To find \( Q3 \) (upper quartile), consider the second half of the data: \( \$1.80, \$1.83, \$1.85, \$2.00 \).

Step2: Calculate \( Q1 \)

For the first - half \( n_1=4 \) (even). \( Q1=\frac{1.60 + 1.64}{2} \).

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Step3: Calculate \( Q3 \)

For the second - half \( n_2 = 4 \) (even). \( Q3=\frac{1.83+1.85}{2} \).

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Answer:

Lower quartile \( (Q1)=\$1.62 \), Upper quartile \( (Q3)=\$1.84 \)