Chapter 12.3, Problem 25P

The lengths of Ana’s last six phone calls were 3 ruin, 19 min, 2 min, 44 min, 120 min, and 4 min. Greg’s last six phone calls were 5 min, 12 min, 4 min, 80 min, 76 min, and 15 min. Find the mean, median, mode, and range of Ana’s calls and Greg’s calls. Use your results to compare each person’s phone call habits.

To determine

Find the mean , median, mode and range of A’s calls and G’s calls.

Answer to Problem 25P

A :

Mean = 32

Median = 11.5

Mode = no mode

Range = 118

G:

Mean=32

Median=13.5

Mode= no mode

Range= 76

Comparison :

1. Mean of both A’s and G’s calls is same.
2. Median of G’s calls is more than that of A’s calls.
3. Both A’s and G’s have no mean of their phone calls.
4. Range of A’s calls is more than that of G’s calls.

Explanation of Solution

Given:

The lengths of A’s last six phone calls were 3 min, 19 min, 2 min , 44 min, 120 min, and 4 min.

G’s last six phone calls were 5 min, 12 min, 4 min, 80 min, 76 min, and 15 min.

Calculation:

Arrange the given data of A’s calls in ascending order :

2 , 3 , 4 , 19 , 44 , 120

Mean = $\frac{sum\text{ of all the entries}}{\text{total number of entries}}=\frac{2+3+4+19+44+120}{6}=\frac{192}{6}=32$

Median = The $\frac{6}{2}=3^{rd}$ and $$ 4^th data value ( since there are 6 entries , which is even) are the middle values , so the median = $\frac{7.2}{2}=\frac{15.6}{2}=7.8$

Mode = The entry that appeares maximum number of times = since all the data values occur only once , so , there is no mode.

Range is the difference of the highest and lowest value of the data =120-2 = 118

Arrange the given data of G’s calls in ascending order :

4 , 5 , 12 , 15 , 76 , 80

Mean = $\frac{sum\text{ of all the entries}}{\text{total number of entries}}=\frac{4+5+12+15+76+80}{6}=\frac{192}{6}=32$

Median = The $\frac{6}{2}=3^{rd}$ and $$ 4^th data value ( since there are 6 entries , which is even) are the middle values , so the median = $\frac{12+15}{2}=\frac{27}{2}=13.5$

Mode = The entry that appeares maximum number of times = since all the data values occur only once , so , there is no mode.

Range is the difference of the highest and lowest value of the data = 80-4 =76

Comparison :

1. Mean of both A’s and G’s calls is same.
2. Median of G’s calls is more than that of A’s calls.
3. Both A’s and G’s have no mean of their phone calls.
4. Range of A’s calls is more than that of G’s calls.