A sample of 28 time shares in the Orlando, Florida, area revealed the following daily charges for a one-bedroom suite. For conve
nience the data are ordered from smallest to largest. Construct a box plot to represent the data. Comment on the distribution. Be sure to identify the first and third quartiles and the median. $116 $121 $157 $192 $207 $209 $209 229 232 236 236 239 243 246 260 264 276 281 283 289 296 307 309 312 317 324 341 353
2 answers:
Response: Median = 253, lower Quartile = 219, Upper quartile = 301.5
Clarification:
Minimum = 116
Average = 253 = the mean indicates the average daily fee. This is determined by adding up all the charges and dividing by the total number of days.
Q1 = 219 = the lower Quartile. This quartile signifies the lowest 25% of the dataset.
Q2 = 253 = Median. The median indicates the midpoint of the dataset, serving as a measure of central tendency.
Q3 = 301.5 = Upper quartile. The upper quartile includes 75% of the data.
Maximum = 353
The box and whisker chart offers a visual grouping of data into quartiles.
The median stands at $253, with this daily charge of $253 for the one-bedroom suite bisecting the dataset (Charges per day) into two equal portions: the lower and upper halves, positioning the $253 charge at the center.
The median equals $253, while the lower quartile is $219 and the upper quartile is 301.5, these figures illustrate that 75% of the daily charges for the suite were around $219. The Box and Whisker Graph demonstrates that for the majority of the days, the charges exceeded $219, leading to a longer lower whisker compared to the upper whisker.
The average charge for a one-bedroom suite aligns with the median, also $253, indicating that the typical daily rate for the suite was $253. With a mean of $253, we can deduce that most daily charges are clustered near this median, thus causing the box and whisker plot to lean towards the right side (upper side), as 50% of the daily rates already surpass $253 with the median at $253.
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