Question

here are the scores of 14 students on an algebra test. 59, 61, 62, 64, 67, 68, 71, 72, 75, 79, 79, 86, 86, 90. notice that the scores are ordered from least to greatest. give the five - number summary and the interquartile range for the data set. five - number summary minimum: lower quartile: median: upper quartile: maximum: interquartile range:

Explanation:

Step1: Find the minimum

The smallest value in the data - set is 59.
59

Step2: Find the maximum

The largest value in the data - set is 90.
90

Step3: Find the median

There are $n = 14$ data points. The median is the average of the $\frac{n}{2}=7$th and $(\frac{n}{2}+1) = 8$th ordered values. So, median$=\frac{71 + 72}{2}=71.5$.
$\frac{71 + 72}{2}=71.5$

Step4: Find the lower half

The lower half of the data set consists of the first 7 values: 59, 61, 62, 64, 67, 68, 71. The median of the lower half (lower quartile $Q_1$) is the 4th value, which is 64.
64

Step5: Find the upper half

The upper half of the data set consists of the last 7 values: 72, 75, 79, 79, 86, 86, 90. The median of the upper half (upper quartile $Q_3$) is the 4th value of this half, which is 79.
79

Step6: Calculate the inter - quartile range

The inter - quartile range (IQR) is $Q_3−Q_1$. So, $IQR=79 - 64=15$.
$79 - 64=15$

Answer:

Minimum: 59
Lower quartile: 64
Median: 71.5
Upper quartile: 79
Maximum: 90
Interquartile range: 15