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A sample of measurements is given: 28 24 26 28 26 26 22 24 Write the empirical distribution law; estimate mode , median, and coefficient ol variation:...

Question

A sample of measurements is given: 28 24 26 28 26 26 22 24 Write the empirical distribution law; estimate mode , median, and coefficient ol variation:

A sample of measurements is given: 28 24 26 28 26 26 22 24 Write the empirical distribution law; estimate mode , median, and coefficient ol variation:



Answers

For the sample data
$$\begin{array}{c|ccccccc} \mathrm{x} & 86 & 27 & 28 & 29 & 30 & 31 & 32 \\ \hline f & 3 & 4 & 16 & 12 & 6 & 2 & 1 \end{array}$$ a. Compute the mean and the standard deviation. b. About how many of the measurements does the Empirical Rule predict will be in the interval $(\bar{x}-n, \bar{x}+n),$ the interval $(\bar{x}-2 \mathrm{n}, \bar{x}+2 \mathrm{n}),$ and the interval $(\bar{x}-3 \mathrm{n}, \overline{\mathrm{x}}+3 \mathrm{n}) ?$ c. Compute the number of measurements that are actually in each of the intervals listed in part (a), and compare to the predicted numbers.

So in this question we are given a sample 1234 were is to find the mean median and mode. So the mean is basically the sum of X divided by N. So we have one, two 34 divided by four. So that's 789 10 divided by four and are mean is 2.5. Now the medium is basically the middle value. And here since we have an even number we take the average of the to middle value. So we have two plus 3/2, That's 2.5. And the mood is basically the the number that appears at the most at the highest frequency within the data said. So the mood, we have all of the numbers appearing At the same frequency. So the mode is basically 1, 2, 3 and four. So we have the mean medium and

So in this question, we are given a sample with four numbers 1-7. So organizing that from lowest to highest, we have 12 two and seven. So to find the mean here you take the average of all the values, So that's 9, 10, 11, 12 divided by four. So our mean is three for the median. We basically take the middle value. So we have to middle values here, so the average of the two middle values is true and the mold is the value that appears the most number of times. So we see the mood here is two.

This question were given six values, so just writing them out, we have minus 10 and we have 111 and four. So we 123456 values minus 10111 and four. And we are asked to find the mean median and mode. So the mean is basically the sum of all the values. So we have four, 567 -1, which is six divided by six. So the mean is one, the median is basically the middle value, so here we have One and one is the middle value, so the median is also one. The mod is the value that appears at the highest frequency, so we have one appearing three times of the mode is also one.

This question, we are asked to create a simple data set of size four where the mean meeting and the mod are all equal. So we have for points here. So let's basically create the median. So let's say the median is one, and we have one appearing twice, so The median is one. The mode is also one. Now the mean here to get the mean to be one, we basically take zero here and two. So we have 4/4, Which is one. So we have our data set Where the mean median and the mode are all one.


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