Question

Find the mean, mode, and range Mean_______ show all workRange_______show all workExplain how you find thisMode_________

Answer 1

To answer this question, it is a good practice to order the data in ascending order as follows:

$9,\: 10,\: 10,\: 10,\: 10,\: 11,\: 11,\: 11,\: 11,\: 11,\: 11,\: 12,\: 12,\: 12,\: 12,\: 12,\: 13,\: 13,\: 13,\: 14,\: 14,\: 15,\: 15,\: 15,\: 15,\: 15,\: 15,16,17,17$

We need to check for the total number of data. In this case, we have 30 observations.

Finding the mean

To find the mean, we need to find the sum of all the observations and then divide this result by the total of observations (30). Then, we have:

$\frac{9+\: 10+\: 10+10+\: 10+\: 11+\: 11+\: 11+\: 11+\: 11+\: 11+\: 12+\: 12+\: 12+\: 12+\: 12+\: 13+\: 13+\: 13+\: 14+\: 14+15+\: 15+\: 15+15+15+_{}15+16+17+17}{30}$

Then, the value for the mean is:

$\text{mean}=\frac{382}{30}=12.73333333\ldots$Finding the range

The range is the result of subtracting the greatest number and the lowest number in the data:

$\text{Range}=17-9=8$Finding the mode

The mode is the observation that is repeated the most (appears the most).

We can see that we have two values that appear six times in the list: 11 and 15.

Therefore, we can see that there is not a unique element, so there is no mode.

In summary, we have:

• Mean = 12.73333...

,

• Range = 8

,

• Mode = None.