Question

sunshine raisin company sells snack - sized boxes of raisins. twenty boxes were randomly selected and the raisins were counted. the results are shown in the list below.
48 49 48 50 48
49 50 51 45 47
46 48 45 49 48
47 51 47 48 46
what is the mean, median, and mode of the sunshine raisin data?
a. 47, 48, 49
c. 49, 48, 47
b. 48, 49, 48
d. 48, 48, 48
please select the best answer from the choices provided

Explanation:

Step1: Calculate the mean

First, find the sum of all the data points:

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The mean \(\bar{x}=\frac{908}{20}=45.4\) (Wait, no, let's re - calculate the sum properly.

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No, wrong again. Let's list them out:

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Sum \(S=(45\times2)+(46\times2)+(47\times3)+(48\times7)+(49\times3)+(50\times2)+(51\times2)\)

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Mean \(\bar{x}=\frac{960}{20}=48\)

Step2: Calculate the median

Since \(n = 20\) (even), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered data.
The ordered data: \(45,45,46,46,47,47,47,48,48,48,48,48,48,49,49,49,50,50,51,51\)
\(\frac{n}{2}=10\), \(\frac{n}{2}+1 = 11\)
The 10th and 11th data points are both 48. Median \(M=\frac{48 + 48}{2}=48\)

Step3: Calculate the mode

The mode is the data point that appears most frequently. The number 48 appears 7 times, which is more frequent than other numbers. So the mode is 48.

Answer:

D. 48, 48, 48