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Math  /  Data & Statistics

Question```latex \text{The accompanying data represent the weights (in grams) of a random sample of 48 M\&M plain candies. Complete parts (a) through (f).} \\ \text{Click the icon to view the weights of the M\&M plain candies.} \\ \text{(a) Determine the sample standard deviation weight.} \\ \text{□\square gram(s)} \\ \text{(Round to three decimal places as needed.)} \\
\text{The user took a picture with their phone and the text was extracted above. The user then had a dialogue with an AI Assistant to help clarify the instructions.} \\
\text{Dialogue Transcript:} \\
\text{assistant:} \\ \text{It looks like you're working on a statistics problem involving the weights of M\&M candies and you need to calculate the sample standard deviation. To help you with this, I need the list of weights you mentioned. Please provide the weights of the 48 M\&M plain candies so I can assist you further.} \\
\text{user:} \\ \text{I uploaded an image and extracted the following:} \\ \text{* Text: \begin{tabular}{llllllll} 0.89 & 0.94 & 0.92 & 0.89 & 0.93 & 0.86 & 0.84 & 0.83 \\ 0.83 & 0.91 & 0.82 & 0.84 & 0.89 & 0.93 & 0.84 & 0.90 \\ 0.91 & 0.95 & 0.86 & 0.85 & 0.79 & 0.91 & 0.88 & 0.84 \\ 0.88 & 0.91 & 0.86 & 0.90 & 0.93 & 0.87 & 0.88 & 0.87 \end{tabular}} \\ \text{Print} \\ \text{Done} ```

Studdy Solution

STEP 1

1. The data set consists of weights of 48 M&M plain candies.
2. The weights provided are in grams.
3. We need to calculate the sample standard deviation, which is a measure of the amount of variation or dispersion in a set of values.

STEP 2

1. Gather the complete data set.
2. Calculate the mean of the data set.
3. Compute the deviations from the mean for each data point.
4. Square each deviation.
5. Sum the squared deviations.
6. Divide the sum by n−1 n-1 to find the variance (where n n is the number of data points).
7. Take the square root of the variance to find the sample standard deviation.
8. Round the result to three decimal places.

STEP 3

Gather the complete data set. The extracted data from the image is:
\[ \begin{align*} 0.89, & \ 0.94, \ 0.92, \ 0.89, \ 0.93, \ 0.86, \ 0.84, \ 0.83, \\ 0.83, & \ 0.91, \ 0.82, \ 0.84, \ 0.89, \ 0.93, \ 0.84, \ 0.90, \\ 0.91, & \ 0.95, \ 0.86, \ 0.85, \ 0.79, \ 0.91, \ 0.88, \ 0.84, \\ 0.88, & \ 0.91, \ 0.86, \ 0.90, \ 0.93, \ 0.87, \ 0.88, \ 0.87 \end{align*}$
Note: The extracted data seems to be incomplete. Ensure all 48 data points are available for accurate calculation.

STEP 4

Assuming the data set is complete, list all 48 weights for calculation.

STEP 5

Calculate the mean (xˉ\bar{x}) of the data set. Sum all the weights and divide by the number of data points (48).
xˉ=∑i=148xi48\bar{x} = \frac{\sum_{i=1}^{48} x_i}{48}

STEP 6

Compute the deviation of each data point from the mean.
Deviation for each xi=xi−xˉ\text{Deviation for each } x_i = x_i - \bar{x}

STEP 7

Square each deviation.
(xi−xˉ)2(x_i - \bar{x})^2

STEP 8

Sum all the squared deviations.
∑i=148(xi−xˉ)2\sum_{i=1}^{48} (x_i - \bar{x})^2

STEP 9

Divide the sum by n−1 n-1 (where n=48 n = 48 ) to find the variance.
s2=∑i=148(xi−xˉ)247s^2 = \frac{\sum_{i=1}^{48} (x_i - \bar{x})^2}{47}

STEP 10

Take the square root of the variance to find the sample standard deviation.
s=s2s = \sqrt{s^2}

STEP 11

Round the result to three decimal places.
The sample standard deviation is approximately:
s \boxed{s}
Note: The exact value of s s requires the complete data set and calculations.

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