Question

knowledge check

on a sheet of paper, write the letter of the correct answer.

1. you have the following set of data: 12, 15, 18, 22, 25. what is the range of this data?

a. 7
b. 10
c. 13
d. 18

1. study this data set: 4, 8, 12, 16, 20. what is the mean deviation of this data set?

a. 4
b. 4.8
c. 6
d. 2.5

1. the ages of five students are 13, 15, 16, 18, and 20. calculate the sample standard deviation (rounded to two decimal places).

a. 2.7
b. 3.16
c. 4.34
d. 5.01

1. if the scores of students in a math test are 45, 50, 55, 60, and 65, what is the range of the scores?

a. 20
b. 15
c. 10
d. 5

1. find the mean deviation of this data: 7, 10, 13, 15, 20.

a. 2.5
b. 4.2
c. 3.6
d. 5.0

1. a sample data has the following values: 2, 4, 6, 8, 10. what is the sample standard deviation?

a. 2.82
b. 3.16
c. 4.00
d. 5.01

Explanation:

Question 1

Step1: Recall range formula

Range is calculated as the difference between the maximum and minimum values in a data set. The formula is \( \text{Range} = \text{Maximum value} - \text{Minimum value} \).

Step2: Identify max and min

For the data set \( 12, 15, 18, 22, 25 \), the maximum value is \( 25 \) and the minimum value is \( 12 \).

Step3: Calculate range

Substitute the values into the formula: \( 25 - 12 = 13 \).

Step1: Find the mean

First, calculate the mean (\( \bar{x} \)) of the data set \( 4, 8, 12, 16, 20 \). The formula for the mean is \( \bar{x} = \frac{\sum_{i = 1}^{n} x_{i}}{n} \), where \( n \) is the number of data points.
\( \sum_{i = 1}^{5} x_{i}=4 + 8+12 + 16+20=60 \), and \( n = 5 \). So, \( \bar{x}=\frac{60}{5}=12 \).

Step2: Calculate absolute deviations

Find the absolute deviation of each data point from the mean:
\( |4 - 12| = 8 \), \( |8 - 12| = 4 \), \( |12 - 12| = 0 \), \( |16 - 12| = 4 \), \( |20 - 12| = 8 \).

Step3: Find the mean of absolute deviations

The mean deviation is the mean of these absolute deviations. The formula is \( \text{Mean Deviation}=\frac{\sum_{i = 1}^{n}|x_{i}-\bar{x}|}{n} \).
\( \sum_{i = 1}^{5}|x_{i}-\bar{x}|=8 + 4+0 + 4+8 = 24 \). Then, \( \text{Mean Deviation}=\frac{24}{5}=4.8 \).

Step1: Find the mean

For the data set \( 13, 15, 16, 18, 20 \), \( n = 5 \).
\( \sum_{i = 1}^{5}x_{i}=13 + 15+16 + 18+20 = 82 \). The mean \( \bar{x}=\frac{82}{5}=16.4 \).

Step2: Calculate squared deviations

Find \( (x_{i}-\bar{x})^{2} \) for each data point:

• \( (13 - 16.4)^{2}=(- 3.4)^{2}=11.56 \)
• \( (15 - 16.4)^{2}=(-1.4)^{2}=1.96 \)
• \( (16 - 16.4)^{2}=(-0.4)^{2}=0.16 \)
• \( (18 - 16.4)^{2}=(1.6)^{2}=2.56 \)
• \( (20 - 16.4)^{2}=(3.6)^{2}=12.96 \)

Step3: Find the sample variance

The sample variance (\( s^{2} \)) is given by \( s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1} \).
\( \sum_{i = 1}^{5}(x_{i}-\bar{x})^{2}=11.56+1.96 + 0.16+2.56+12.96 = 29.2 \).
\( n-1 = 4 \), so \( s^{2}=\frac{29.2}{4}=7.3 \).

Step4: Find the sample standard deviation

The sample standard deviation (\( s \)) is the square root of the sample variance: \( s=\sqrt{7.3}\approx2.7 \) (rounded to two decimal places).

Answer:

C

Question 2