Question

A researcher observed how many glasses of water the participants in his study drank in a day. He recorded that the 8 participants drank 4, 3, 9, 8, 5, 7, 16, and 4 glasses. Report the mean, median, and mode for this data. Would the mean or median be more representative of the data?

a) Mean: 7; Median: 6; Mode: 4; Median is more representative.
b) Mean: 7; Median: 7; Mode: 8; Mean is more representative.
c) Mean: 6; Median: 7; Mode: 4; Mode is more representative.
d) Mean: 7; Median: 5; Mode: 8; Both mean and median are equally representative.

Answer 1

After calculating the mean, median, and mode of the data set, the mean is 7, the median is 6, and the mode is 4. The median is deemed more representative due to the presence of an outlier. the correct option is:

a) Mean: 7; Median: 6; Mode: 4; Median is more representative.

Step-by-step explanation:

The student is asking to find the mean, median, and mode for a data set and determine which of these measures of central tendency is more representative of the data provided.

First, let's calculate the mean (arithmetic average). We sum all the glasses of water consumed and divide by the number of participants:

(4 + 3 + 9 + 8 + 5 + 7 + 16 + 4) ÷ 8 = 56 ÷ 8 = 7

Next, we arrange the data in ascending order to find the median (the middle number in a sorted list):

• 3, 4, 4, 5, 7, 8, 9, 16

With 8 numbers, the median will be the average of the 4th and 5th numbers:

(5 + 7) ÷ 2 = 12 ÷ 2 = 6

Now, let's find the mode (most frequently occurring number). In this data set, the number 4 occurs twice, and no other number occurs more than once, making 4 the mode.

The mean is 7, the median is 6, and the mode is 4. Considering that the data contains an outlier (16 glasses), the median might be a more representative measure of central tendency because it is less affected by extreme values. Therefore, the correct option is:

a) Mean: 7; Median: 6; Mode: 4; Median is more representative.