Question

1. what is the sample standard deviation for the data given: 5, 10, 7, 12, 0, 20, 15, 22, 8, 2

a) 6.89
b) 9
c) 10.1
d) 7.26

1. all of the below sets have the same mean.

set 1 - standard deviation=3.1
set 2 - standard deviation=4.9
set 3 - standard deviation=1.7
set 4 - standard deviation=3.2
which set of data probably has the points closest to the mean?
a) 2
b) 4
c) 3
d) 1

1. four data sets are shown below.

set 1: {10, 19, 38, 50, 51}
set 2: {5, 21, 26, 39, 51}
set 3: {9, 38, 50, 50, 51}
set 4: {5, 28, 28, 28, 51}
which data set has the largest standard deviation?
a) set 2
b) set 1
c) set 4
d) set 3

1. how many values are within one standard deviation of the mean? 180, 313, 101, 255, 202, 198, 109, 183, 181, 113, 171, 165, 318, 145, 131, 145, 226, 113, 268, 108

a) 12
b) 10
c) 11
d) 9

Explanation:

Step1: Calculate mean for first - question data

The data set is \(5, 10, 7, 12, 0, 20, 15, 22, 8, 2\). The mean \(\bar{x}=\frac{5 + 10+7+12+0+20+15+22+8+2}{10}=\frac{101}{10} = 10.1\).

Step2: Calculate squared - differences

\((5 - 10.1)^2=(- 5.1)^2 = 26.01\), \((10 - 10.1)^2=(-0.1)^2 = 0.01\), \((7 - 10.1)^2=(-3.1)^2 = 9.61\), \((12 - 10.1)^2=(1.9)^2 = 3.61\), \((0 - 10.1)^2=(-10.1)^2 = 102.01\), \((20 - 10.1)^2=(9.9)^2 = 98.01\), \((15 - 10.1)^2=(4.9)^2 = 24.01\), \((22 - 10.1)^2=(11.9)^2 = 141.61\), \((8 - 10.1)^2=(-2.1)^2 = 4.41\), \((2 - 10.1)^2=(-8.1)^2 = 65.61\).

Step3: Calculate variance

The variance \(s^{2}=\frac{26.01+0.01 + 9.61+3.61+102.01+98.01+24.01+141.61+4.41+65.61}{9}=\frac{474.9}{9}\approx52.77\).

Step4: Calculate standard deviation

The sample standard deviation \(s=\sqrt{52.77}\approx7.26\).

For the second question, the smaller the standard deviation, the closer the data points are to the mean. Since Set 3 has the smallest standard - deviation (\(1.7\)), the answer is c).

For the third question, we can estimate the spread of the data sets. Set 1 has values that are more spread out from each other compared to the other sets. The larger the spread of data, the larger the standard deviation. So the answer is b).

For the fourth question, we first need to calculate the mean and standard deviation of the data set \(180,313,101,255,202,198,109,183,181,113,171,165,318,145,131,145,226,113,268,108\). But we can also make a rough estimate. After calculating the mean \(\bar{x}\) and standard deviation \(s\) (or by rough - comparison), we find the number of values within one standard deviation of the mean. After calculation, we find there are 11 values within one standard deviation of the mean, so the answer is c).

Answer:

1. d) 7.26
2. c) 3
3. b) Set 1
4. c) 11