Question

story based interquartile ranges worksheet 1

1. julia had recorded her last 6 math test scores. answer these questions based on the test scores {93,98,75,86,79,92}.

quartile 1____ quartile 3____
median____ interquartile range____

Explanation:

Step1: Sort the data

Sort the test - scores in ascending order: $75,79,86,92,93,98$.

Step2: Find the median

Since there are $n = 6$ data points, the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. $\frac{6}{2}=3$ and $\frac{6}{2}+1 = 4$. Median$=\frac{86 + 92}{2}=89$.

Step3: Find Quartile 1

The lower half of the data is $75,79,86$. Since there are $n_1=3$ data points in the lower - half, the first quartile $Q_1$ is the middle value of the lower - half, so $Q_1 = 79$.

Step4: Find Quartile 3

The upper half of the data is $92,93,98$. Since there are $n_2 = 3$ data points in the upper - half, the third quartile $Q_3$ is the middle value of the upper - half, so $Q_3=93$.

Step5: Calculate the interquartile range

Interquartile range (IQR) is $Q_3−Q_1$. So, $IQR=93 - 79=14$.

Answer:

Quartile 1: $79$
Quartile 3: $93$
Median: $89$
Interquartile Range: $14$