Question

answer the statistical measures and create a box and whiskers plot for the following set of data. enter all values as whole numbers or decimals. 3,4,4,5,7,7,10,10,12,16 min: q1: med: q3: max: create the box plot by dragging the lines:

Explanation:

Step1: Find minimum value

The minimum value in the data - set $3,4,4,5,7,7,10,10,12,16$ is $3$.

Step2: Find first quartile (Q1)

First, find the median of the lower half of the data. The data set has $n = 10$ values. The lower half is $3,4,4,5,7$. The median of this lower - half (Q1) is the middle value. Since there are 5 values, the median of the lower half is $4$.

Step3: Find median (Med)

Since $n = 10$ (an even number of values), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. $\frac{10}{2}=5$ and $\frac{10}{2}+1 = 6$. The 5th and 6th values are $7$ and $7$, so the median is $\frac{7 + 7}{2}=7$.

Step4: Find third quartile (Q3)

The upper half of the data is $7,10,10,12,16$. The median of this upper - half (Q3) is the middle value. Since there are 5 values, the median of the upper half is $10$.

Step5: Find maximum value

The maximum value in the data - set is $16$.

Answer:

Min: $3$
Q1: $4$
Med: $7$
Q3: $10$
Max: $16$