Question

Find the mean median and mode of the data set round to the nearest tenth 12 23 17 20 14 14 18 16 17 18 18

Answer 1

For the given data set,

12,23,17,20,14,14,18,16,17,18,18

We have to determine the mean, median and mode.

Mean is calculated by the " sum of all the observations divided by the total number of observations".

First of all, let us arrange the numbers in ascending order.

12, 14, 14, 16, 17, 17, 18, 18, 18, 20, 23

Mean = $\frac{12+14+14+16+17+17+18+18+18+20+23}{11}$

Mean = $\frac{187}{11}$

Mean = 17

So, the mean of the data set is 17.

The mode of a set of numbers is the one that occurs most often.

Since, we observe that '18' is a number among the data set which occurs often.

Therefore, mode of the data set is 18.

Now, we will calculate median.

Since there are 11 terms. Since 11 is an odd number.

Median = $\frac{n+1}{2}$th observation

= $\frac{11+1}{2}$

= 6th observation

From the arranged data set, the 6th observation is 17.

So, the median of the data set is 17.

Hence, Mean = 17

Mode = 18

Median = 17