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.
Which part of this problem don't you understand?
http://www.purplemath.com/modules/meanmode.htm
To compute the sample mean, add up all the numbers in the data set, and then divide the sum by the total number of values. In this case, the data set consists of 16 values:
142 + 171 + 125 + 91 + 140 + 125 + 97 + 125 + 162 + 142 + 125 + 117 + 89 + 125 + 140 + 128 = 2064
Next, divide this sum by 16:
Mean = 2064/16 = 129
Therefore, the sample mean is 129.
To find the median, first arrange the data set in ascending order:
89 91 97 117 125 125 125 125 128 140 140 142 142 162 171
Since there are 16 values in the data set, the median will be the average of the middle two values. In this case, the middle two values are 125 and 128. So, the median is:
Median = (125 + 128) / 2 = 126.5
The mode is the value that appears most frequently in the data set. From the data set, the value 125 appears the most, as it occurs 4 times. Thus, the mode is 125.
The midrange is the average of the highest and lowest values in the data set. Here, the lowest value is 89 and the highest value is 171. So, the midrange is:
Midrange = (89 + 171) / 2 = 130
To compute the 1st quartile, we need to find the median of the lower half of the data set. Since there are 16 values, the 1st quartile will be the median of the first 8 values. In this case, the first 8 values are:
89 91 97 117 125 125 125 125
To find the median of these 8 values, we calculate the average of the middle two values, which are 97 and 117. So, the 1st quartile is:
Q1 = (97 + 117) / 2 = 107
The 1st quartile represents the point below which 25% of the data falls. In this case, it means that 25% of the dry cleaning orders picked up at Sunny Fresh Dry Cleaners were below 107.
Similarly, to compute the 3rd quartile, we find the median of the upper half of the data set. The last 8 values in the data set are:
128 140 140 142 142 162 171
The median of these 8 values is the average of the middle two values, which are 142 and 142. So, the 3rd quartile is:
Q3 = (142 + 142) / 2 = 142
The 3rd quartile represents the point below which 75% of the data falls. In this case, it means that 75% of the dry cleaning orders picked up at Sunny Fresh Dry Cleaners were below 142.
In summary:
Sample Mean: 129
Median: 126.5
Mode: 125
Midrange: 130
1st Quartile (Q1): 107
3rd Quartile (Q3): 142