A manufacturer of elevators would like to recalibrate the weight limit and passenger limit of one of the elevators they have installed in a building. To help with the recalibration process, they have decided to collect some data. Among people who took the elevator and who also consented to provide data for the recalibration process, a random sample of 9 people were selected and the weight (in kilograms) of each person was recorded. The weights are listed below:50, 86, 41, 52, 44, 31, 61, 63, 81Using the formula given in lectures, calculate the interquartile range of these weights. Do not include any units in your answer.
Question
A manufacturer of elevators would like to recalibrate the weight limit and passenger limit of one of the elevators they have installed in a building. To help with the recalibration process, they have decided to collect some data. Among people who took the elevator and who also consented to provide data for the recalibration process, a random sample of 9 people were selected and the weight (in kilograms) of each person was recorded. The weights are listed below:50, 86, 41, 52, 44, 31, 61, 63, 81Using the formula given in lectures, calculate the interquartile range of these weights. Do not include any units in your answer.
Solution
The interquartile range (IQR) is a measure of statistical dispersion and is calculated as the difference between the upper quartile (Q3) and the lower quartile (Q1).
First, we need to sort the data in ascending order: 31, 41, 44, 50, 52, 61, 63, 81, 86.
Next, we find Q1 and Q3. Since there are 9 data points:
-
Q1 is the median of the first half of the data (not including the overall median if the number of data points is odd). The first half of the data is 31, 41, 44, 50. The median is the average of 41 and 44, which is 42.5.
-
Q3 is the median of the second half of the data. The second half of the data is 61, 63, 81, 86. The median is the average of 63 and 81, which is 72.
Finally, we subtract Q1 from Q3 to find the IQR: 72 - 42.5 = 29.5.
So, the interquartile range of these weights is 29.5.
Similar Questions
How can you find a representative value for each interval? Should each interval be given equal weight when calculating the mean?
Weights. I sample 7 random males in the US and record their weights in pounds. Some of their data are given below.149 178 202 206 213 220 252Find a 98% confidence interval for the mean weight of all US males. (Round to one decimal place)(,)
A man of weight 80 kg is standing in an elevator which is moving with an acceleration of 6 m/s2 in upward direction. The apparent weight of the man will be (g = 10 m/s2).A 1480 N B 1280 N C 1380 N D 2520 N
The weights in kg of 10 students are given below:39, 43, 36, 38, 46, 51, 33, 44, 44, 43Find the mode of this data.
The weight of 12 students(in kg) are:40, 61, 54, 50, 59, 37, 51, 41, 48, 62, 46 and 34.(i) Calculate the mean weight and the median weight.(ii) After 6 months the weight of each student increases by 4 kg, find thenew mean weight.(iii) If the weight of one students was misread as 34 instead of 28, findthe correct median weight.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.