Question

1. based on the dot - plot below, list all of the values in the data set below:

0 1 2 3 4 5
number of pets
which statement about the data is correct?
(1) the mean and the median are the same.
(2) the median and the mode are the same.
(3) the mean and the mode are the same.
(4) the mean, median, and mode are all the same.
unit 1 lesson 12 cumulative practice problems

1. the shoe size for all the pairs of shoes in a persons closet are recorded.

7 7 7 7 7 7 7 7 7 7
a. what is the mean?
b. what is the standard deviation?

Explanation:

Step1: List values from dot - plot

From the dot - plot, the data set is: 0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5

Step2: Calculate the mean

The mean $\bar{x}=\frac{0 + 3\times1+5\times2 + 3\times3+3\times4 + 1\times5}{16}=\frac{0 + 3+10 + 9+12 + 5}{16}=\frac{39}{16}=2.4375$

Step3: Calculate the median

Arrange the data in ascending order: 0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5. Since $n = 16$ (even), the median is the average of the 8th and 9th values. Median $=\frac{2 + 2}{2}=2$

Step4: Calculate the mode

The mode is the most frequently occurring value. The mode is 2 (it appears 5 times)

For the shoe - size data set {7, 7, 7, 7, 7, 7, 7, 7, 7, 7}:

Step5: Calculate the mean of shoe - size data

The mean $\bar{x}=\frac{10\times7}{10}=7$

Step6: Calculate the standard deviation of shoe - size data

Since all values are 7, the deviation of each value from the mean is 0. The standard deviation $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n}}=\sqrt{\frac{10\times(7 - 7)^{2}}{10}} = 0$

For the dot - plot data:
The mode is 2, the median is 2, and the mean is 2.4375. So the median and the mode are the same.

Answer:

For the dot - plot data: (2)
For the shoe - size data:
a. 7
b. 0