Question

Find the? mean, median, and mode of the set of values. Age? (years) 11 12 13 14 15 16 17 Frequency 7 9 11 10 9 4 3 Find the mean. Select the correct choice below? and, if? necessary, fill in the answer box to complete your choice. The mean is approximately nothing years. ?(Round to two decimal places as? needed.)

Answer 1

Answers:

Mean = 13.55

Median = 13

Mode = 13

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Explanations

Mean:

To get the mean, multiply the ages with their corresponding frequencies. Then add up the results. I show this in the attached image below. The highlighted yellow cell is the sum of the x*y column (x = age, y = frequency). This value is 718.

Once you get to 718, you divide this over the total frequency which is 7+9+11+10+9+4+3 = 53 (so there is 53 people).

The mean is therefore 718/53 = 13.5471698113208 which rounds to 13.55

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Median:

The median is the middle most value. There are 53 values here (add up the frequencies), so the midpoint is at slot 53/2 = 26.5 = 27. The first 26 values are below the median, and the last 26 values are above the median leaving 53-26-26 = 53 - 52 = 1 value in the very exact center.

Add up the frequencies starting from 7 then to 9, etc until you get to 27. So we have

7+9 = 16 which isn't 27

7+9+11 = 16+11 = 27 perfect, we landed on 27

This means that the last copy of 13 is in slot 27. This is because the last frequency added (11) corresponds to the age 13.

That is why the median is 13

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Mode:

The mode is the most frequent value. Simply record the age that has the highest frequency. In this case, the highest frequency is 11 which corresponds to age 13, pointing to the mode being 13.