Question

8. Which box-and-whisker plot shows the high temperatures in Philadelphia, Pennsylvania, during the first two weeks of March: 42, 51, 54, 46, 49, 53, 52, 37, 33, 36, 50, 41, 50, 38

Answer 1

Step 1: Arrange the data given in ascending order, that is from least to greatest.

Given data:

$42, \; 51, \; 54, \; 46,\; 49, \; 53,\; 52, \; 37, \; 33, \; 36, \; 50, \; 41,\; 50,\; 38$

Data in ascending order:

$33, \; 36, \; 37, \; 38, \; 41, \; 42,\; 46, \; 49,\; 50, \; 50,\; 51,\; 52,\; 53, \; 54$

Step 2: Find the median (Q2). The median is the value exactly in the middle of an ordered set of numbers .If there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middlemost numbers.

Since in our problem we have 14 datas, we need to pick the middle most numbers and find the average of the same.

$Median =\frac{46+49}{2} =\frac{95}{2} =47.5$

The median is called Q2 and equal to 47.5

Step 3: Find the lower quartile (Q1). Considering the values to the left of the median(Q2), the median to those values is the Q1 and called as Lower quartile.

$Q1=38$

Step 4: Find the upper quartile (Q3). Considering the values to the right of the median(Q2), the median to those values is the Q3 and called as Upper quartile.

$Q3=51$

Conclusion:

Using the above details we need to plot the box and whisker plot attached with this problem.