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....
mean: 2044/127.75
median: 8 + 9 = 17/2 = 8.5
mode: 125
Range: 73??
mean: You added correctly, but did not divide by the total number of numbers.
http://www.mathgoodies.com/lessons/vol8/mean.html
median. Certainly 8.5 cannot be the median.
http://www.mathgoodies.com/lessons/vol8/median.html
mode: correct
range: wrong
http://www.mathgoodies.com/lessons/vol8/range.html
the mean is 2044/16 = 127.75
the median is 125 + 125 = 250/2 = 125
the range is 171 - 89 = 82
Am i correct?
Right! :-)
yay!! thanks!! but what about the second part:
Compute the 1st
quartile and 3rd and interpret their meanings.
?? im confused
http://www.onlinemathlearning.com/quartile.html
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.
is that correct??
To find the mean, you need to sum up all the values in the dataset and divide it by the total number of values. In this case, the sum of the dry cleaning orders is:
142 + 171 + 125 + 91 + 140 + 125 + 97 + 125 + 162 + 142 + 125 + 117 + 89 + 125 + 140 + 128 = 2044
Since there are 16 values in the dataset, you divide the sum by 16:
Mean = 2044 / 16 = 127.75
To find the median, you need to arrange the values in ascending order and find the middle value. In this case, the data sequence is already sorted as:
89, 91, 97, 117, 125, 125, 125, 125, 128, 140, 140, 142, 142, 162, 171
Since there are 16 values, the median is the average of the two middle values, which are the 8th and 9th values: 125 and 128.
Median = (125 + 128) / 2 = 253 / 2 = 126.5
The mode is the value that appears most frequently in the dataset. In this case, the mode is 125 since it appears 4 times.
The midrange is the average of the maximum and minimum values in the dataset. The highest value is 171, and the lowest value is 89.
Midrange = (171 + 89) / 2 = 260 / 2 = 130
Now, let's move on to the quartiles. The first quartile(Q1) represents the value below which 25% of the data falls, and the third quartile(Q3) represents the value below which 75% of the data falls.
To find the quartiles, you need to arrange the values in ascending order again:
89, 91, 97, 117, 125, 125, 125, 125, 128, 140, 140, 142, 142, 162, 171
To find Q1, you need to find the median of the lower half of the dataset. In this case, the lower half is:
89, 91, 97, 117, 125, 125, 125, 125
Since there are 8 values, the median of the lower half is the average of the 4th and 5th values: 117 and 125.
Q1 = (117 + 125) / 2 = 242 / 2 = 121
To find Q3, you need to find the median of the upper half of the dataset. In this case, the upper half is:
128, 140, 140, 142, 142, 162, 171
Since there are 7 values, the median of the upper half is the average of the 4th value: 142.
Q3 = 142
Interpreting the quartiles:
- Q1 (121) represents the value below which 25% of the dry cleaning orders are less than or equal to.
- Q3 (142) represents the value below which 75% of the dry cleaning orders are less than or equal to.
Hope this helps!