4. 0 / 1 points a statistics student wanted to investigate the weights of bags of a popular chocolate candy…
4. 0 / 1 points a statistics student wanted to investigate the weights of bags of a popular chocolate candy. the data for the weights of the bags, in ounces, are given below. which of the following boxplots correctly displays the data? 1.78 1.68 1.86 1.72 1.70 1.77 1.84 1.73 1.72 1.77 1.74 1.71 1.79 1.77 1.74 1.73 1.68 1.72 1.69 1.78 1.75 1.75 1.81 1.74 details my notes previous answers
Answer
Explanation:
Step1: Arrange data in ascending order
1.68, 1.69, 1.70, 1.71, 1.72, 1.72, 1.72, 1.73, 1.73, 1.73, 1.74, 1.74, 1.74, 1.75, 1.75, 1.77, 1.77, 1.77, 1.78, 1.78, 1.78, 1.79, 1.81, 1.84, 1.86
Step2: Find the median (Q2)
Since there are (n = 25) data - points, the median is the (\left(\frac{n + 1}{2}\right))-th value. (\frac{25+1}{2}=13) - th value. So (Q2=1.74).
Step3: Find the lower half and Q1
The lower half of the data has 12 values. The median of the lower half (Q1) is the average of the 6 - th and 7 - th ordered values. The 6 - th value is 1.72 and the 7 - th value is 1.72, so (Q1 = 1.72).
Step4: Find the upper half and Q3
The upper half of the data has 12 values. The median of the upper half (Q3) is the average of the 19 - th and 20 - th ordered values. The 19 - th value is 1.78 and the 20 - th value is 1.78, so (Q3 = 1.78).
Step5: Find the minimum and maximum
The minimum value is 1.68 and the maximum value is 1.86.
Step6: Check box - plots
A correct box - plot will have the box from (Q1 = 1.72) to (Q3 = 1.78), a line inside the box at (Q2=1.74), whiskers extending to 1.68 and 1.86 (with no outliers calculated using the (1.5\times IQR) rule for simplicity here as we are mainly focused on the position of box and median line).