Question

adults who are being tested for dementia are asked to perform mental tasks such as listing as many animals as they can in one minute. here are the numbers of animals listed in one minute by 10 adults: 16, 12, 17, 18, 21, 11, 22, 13, 19, 10

(a) what is the median of this data set? if your answer is not an integer, round your answer to one decimal place.

(b) what is the mean of this data set? if your answer is not an integer, round your answer to one decimal place.

(c) how many modes does the data set have, and what are their values? indicate the number of modes by clicking in the appropriate circle, and then indicate the value(s) of the mode(s), if applicable.

options for number of modes: zero modes, one mode, two modes

Explanation:

Step1: Organize the data set

First, we need to sort the data set. The given data is: 16, 12, 17, 18, 21, 11, 22, 13, 19, 10. Sorting it in ascending order: 10, 11, 12, 13, 16, 17, 18, 19, 21, 22.

Step2: Find the median (a)

The median is the middle value of a sorted data set. Since there are 10 (an even number) values, the median is the average of the 5th and 6th values. The 5th value is 16 and the 6th value is 17. So, the median is $\frac{16 + 17}{2} = \frac{33}{2} = 16.5$.

Step3: Find the mean (b)

The mean is calculated by summing all the values and dividing by the number of values. The sum of the data set: $10 + 11 + 12 + 13 + 16 + 17 + 18 + 19 + 21 + 22$. Let's calculate the sum: $10+11 = 21$; $21+12 = 33$; $33+13 = 46$; $46+16 = 62$; $62+17 = 79$; $79+18 = 97$; $97+19 = 116$; $116+21 = 137$; $137+22 = 159$. The number of values is 10. So the mean is $\frac{159}{10} = 15.9$.

Step4: Find the mode (c)

The mode is the value that appears most frequently. In this data set, each value appears only once. So, there are zero modes.

Answer:

s:
(a) The median is 16.5.
(b) The mean is 15.9.
(c) The data set has zero modes.