Question

The number of writing instruments in some teachers' desks is displayed in the dot plot. Which is greater the mean or the median? Explain your reasoning using the shape of the distribution.

please help..
30 points

Answer 1

The median is greater than the mean. From the shape of the distribution, the data set has more values on the left, so we can say it is skewed to the left. In every distribution that is skewed to the left, the median is always greater than the mean.

In the given chart we can deduce the following;

• number of instruments that is 5 = 1

• number of instruments that is 6 = 1

• number of instruments that is 7 = 1

• number of instruments that is 8 = 1

• number of instruments that is 9 = 3

• number of instruments that is 10 = 4

• number of instruments that is 11 = 2

• number of instruments that is 12 = 1

These numbers can be listed as follows;

5, 6, 7, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 12

The median of these numbers is calculated as;

$median = \frac{9+ 10}{2} = 9.5$

The mean of these numbers is calculated as;

$mean = \frac{5+6+7+8+9+9+9+10+10+10+10+11+11+12}{14} = 9.07$

Thus, the median is greater than the mean.

Also, from the shape of the distribution, the data set has more values on the left, so we can say it is skewed to the left. In every distribution that is skewed to the left, the median is always greater than the mean. But if the distribution is skewed to the right, the mean is always greater than the median.

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