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zach6024
05.05.2020 •
Mathematics
3. There are 350 people in an office building. A local deli randomly surveyed people in the building to determine the average amount spent on lunch each week. Two samples are shown.
Sample 1: {$30, $25, $10, $25, $10} and Sample 2: {$5, $60, $10, $30, $50}
(a) Calculate the mean and the median of each sample.
(b) Which sample has the least spread among its data values? Which sample has the least deviations from the mean among its values?
(c) A third sample was obtained: {$30, $25, $20, $20, $25}. Which data set in Part (a) has measures of center that align more closely with the mean and the median of the new sample? Based on the three samples, which sample is least representative of the population?
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Ответ:
(a)Sample 1
The Mean = 20
The median = 25
Sample 2
The Mean = 31
The median = 60
(b) Sample 1 has the least spread
Sample 1 has the least deviations from the mean
(c) Sample 1 align with the third sample
The least representative of the population is sample 1
Step-by-step explanation:
The mean is ∑fx/∑f
∑fx = 30 + 25 + 10 + 25 + 10 = 100
∑f = 5
Mean = 100/5 = 20
For the median, we arrange the data in increasing order;
10, 10, 25, 25, 30
The median = the middle number = 25
Sample 2
The mean is ∑fx/∑f
∑fx = 5 + 60 + 10 + 30 + 50 = 155
∑f = 5
Mean = 155/5 = 31
For the median, we arrange the data in increasing order;
5, 10, 30, 50, 60
The median = the middle number = 30
(b) Sample 1 range =$30 -$10 = $20
Sample 2 range =$65 -$5 = $60
Sample 1 has the least spread
Sample 1 standard deviation = 9.354
Sample 2 standard deviation =24.083
Sample 1 has the least deviations from the mean
(c) $30, $25, $20, $20, $25
Mean = 24
$20, $20, $25, $25, $30
Median = $25
∑fx = 120
Therefore sample 1 align with the third sample
The least representative of the population is sample 1 with ∑fx = 100.
Ответ: