Question

answer the questions below.
(a) as part of the u.s. census, the number of children is reported for each family in the u.s. which measure gives the most common number of children for a u.s. family?
mean
median
mode
(b) in a survey, 10 people reported how many soft drinks they drank in the last month. here are their responses:
28, 29, 31, 32, 33, 35, 36, 37, 38, 39.
which measure should be used to summarize the data?
mean
median
mode
(c) in the past 9 days, amy has received the following numbers of email advertisements per day:
42, 43, 44, 45, 46, 47, 50, 52, 85.
which measure should be used to summarize the data?
mean
median
mode

Explanation:

(a)

Step1: Recall the definition of mode

The mode is the value that appears most frequently in a data set. When we want to find the most common number (the one that occurs more often than others), the mode is the appropriate measure.

(b)

Step1: Check for symmetry and outliers

The data set \(28,29,31,32,33,35,36,37,38,39\) has no extreme values (outliers) and is relatively symmetric. The mean is calculated as \(\frac{28 + 29+31+32+33+35+36+37+38+39}{10}=\frac{338}{10} = 33.8\). The median for \(n = 10\) (even number of data points) is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+ 1)\)th ordered values. The \(\frac{10}{2}=5\)th value is \(33\) and the \((\frac{10}{2}+1) = 6\)th value is \(35\), so the median is \(\frac{33 + 35}{2}=34\). Since the data is relatively symmetric, the mean is a good measure.

(c)

Step1: Identify outliers

The data set \(42,43,44,45,46,47,50,52,85\) has an outlier (\(85\)). The mean is \(\frac{42+43+44+45+46+47+50+52+85}{9}=\frac{454}{9}\approx50.44\). The median for \(n = 9\) (odd number of data points) is the \(\frac{n + 1}{2}\)th ordered value. \(\frac{9+1}{2}=5\)th value. When the data is ordered \(42,43,44,45,46,47,50,52,85\), the median is \(46\). Since there is an outlier, the median is less affected by the outlier than the mean.

Answer:

(a) Mode
(b) Mean
(c) Median