Question

A teacher asks her class of 22 students, "What is your age?" Their responses are shown below.

19, 19, 14, 14, 16, 19, 19, 16, 16, 15, 17, 16, 17, 16, 15, 14, 15, 15, 17, 14, 16, 15
Find the mean, median, and mode for the data. If necessary, round to the nearest tenth.
O A 16.5; 17; 17
OB. 16.1: 16; 16
C. 16.1; 17; 16
o
D. 16.5; 16; 17

Answer 1

B.

Mean: 16.1

Median: 16

Mode: 16

Explanation:

First, order the numbers in the data set from least to greatest:

`14 , 14 , 14 , 14 , 15 , 15 , 15 , 15 , 15 , 16 , 16 , 16 , 16 , 16 , 16 , 17 , 17 , 17 , 19 , 19 , 19 , 19`

First, find the mean. The mean of a data set can be found by adding all the numbers together and dividing by the amount of numbers in the set:

`(14 + 14 + 14 + 14 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 16 + 16 + 16 + 16 + 17 + 17 + 17 + 19 + 19 + 19 + 19)/(22) = (354)/(22)`

Next, simplify by dividing:

`(354)/(22) = (177)/(11) = 16 (1)/(11) or ~16.1`

Mean: 16.1

Next, find the median. The median is the number(s) directly in the middle. If there is a even amount of number in the data set, find the mean of the two median numbers:

Median: 16 , 16

Median =
`(16 + 16)/(2) = (32)/(2) = 16`

Median = 16

Next, find the mode. The median is the number that shows up the most. In this case, it is 16, which appears 6 times, 1 more time then the next number that appears the most 15, which appears 5 times.

Mode: 16

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If you are asked about range, range would be the greatest digit value subtracted by the least digit value. In this case, it would be 14 & 19:

19 - 14 = 5

Range: 5

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