The number of dry cleaning orders picked up at Sunny Fresh Dry Cleaners was sampled over 12 hour periods. Below is the sample:
142 171 125 91 140 125 97 125 162 142 125 117 89 125 140 128
From this data set, compute the sample mean, median, mode and midrange. Compute the 1st
quartile and 3rd and interpret their meanings.
I'm pretty sure i did this part correct, but im confused with the second part....
the mean is 2044/16 = 127.75
the median is 125 + 125 = 250/2 = 125
the range is 171 - 89 = 82
The 1st quartile (lower quartile) is 34 and the 3rd quartile (upper quartile) is 61. The lower quartile is the middle value of the lower half. The upper quartile is the middle value of the upper half.
How can a quartile be less than any of your data?
Study this site about quartiles. You should also study your text materials.
http://www.onlinemathlearning.com/quartile.html
You can also use this site.
http://www.alcula.com/calculators/statistics/quartiles/
The mean, median and the range are correct.
Don't know how you got 34 and 61 for the quartiles when the minimum value is 89.
Your definition of the quartiles is correct, although in practice there might be different ways to calculate them.
I apologize Ms. Sue, I was reading the wrong problem...I believe the 1st quartile is 117 and the 3rd quartile is 140....am i correct??
Jen -- Please THINK and PROOFREAD before you post your questions!!!!!
I did....how is that incorrect???
There are 16 observations, so the median is the mean of the two middle numbers, namely 125 and 125, which you did correctly.
The lower quartile is the median of the lower half, excluding the median, meaning the median of the lower eight observations. This works out to be the mean of 117 and 125 = 121.
The upper quartile can be worked out similarly. So work it out and post for confirmation if you wish.
To compute the first and third quartiles, you need to arrange the data in ascending order:
89, 91, 97, 117, 125, 125, 125, 125, 128, 140, 140, 142, 142, 162, 171
Since there are 16 data points, the first quartile is the median of the lower half and the third quartile is the median of the upper half.
The first quartile is the value that divides the lower half into two equal parts. In this case, the lower half contains 8 data points: 89, 91, 97, 117, 125, 125, 125, 125. To find the median of these data points, you need to calculate the average of the two middle values, which are 97 and 117. Therefore, the first quartile is (97 + 117)/2 = 107.
The third quartile is the value that divides the upper half into two equal parts. In this case, the upper half also contains 8 data points: 128, 140, 140, 142, 142, 162, 171. Similarly, you need to calculate the average of the two middle values, which are 142 and 142. So, the third quartile is (142 + 142)/2 = 142.
The first quartile (Q1) indicates that 25% of the data is below 107. In this case, it means that 25% of the 12-hour periods had fewer than 107 dry cleaning orders.
The third quartile (Q3) indicates that 75% of the data is below 142. In other words, 75% of the 12-hour periods had fewer than 142 dry cleaning orders.
Interpreting the quartiles helps understand the distribution of the data and provides insights into how the dry cleaning orders are distributed during the sampled periods.