Math / Data & Statistics

QuestionFind the range and standard deviation of the set of data. $11,8,7,13,21 \square$
The range is $\square$ (Simplify your answer.)

Studdy Solution

STEP 1

1. The data set consists of the numbers: $11, 8, 7, 13, 21$ .
2. The range is the difference between the maximum and minimum values in the data set.
3. The standard deviation measures the amount of variation or dispersion in a set of values.

STEP 2

1. Calculate the range.
2. Calculate the standard deviation.

STEP 3

Identify the maximum and minimum values in the data set:
Maximum value = $21$
Minimum value = $7$

STEP 4

Calculate the range by subtracting the minimum value from the maximum value:
$\text{Range} = 21 - 7 = 14$

STEP 5

Calculate the mean (average) of the data set:
$\text{Mean} = \frac{11 + 8 + 7 + 13 + 21}{5} = \frac{60}{5} = 12$

STEP 6

Calculate the squared differences from the mean for each data point:
$(11 - 12)^2 = 1$
$(8 - 12)^2 = 16$
$(7 - 12)^2 = 25$
$(13 - 12)^2 = 1$
$(21 - 12)^2 = 81$

STEP 7

Calculate the variance by finding the average of the squared differences:
$\text{Variance} = \frac{1 + 16 + 25 + 1 + 81}{5} = \frac{124}{5} = 24.8$

STEP 8

Calculate the standard deviation by taking the square root of the variance:
$\text{Standard Deviation} = \sqrt{24.8} \approx 4.98$
The range is:
$\boxed{14}$
The standard deviation is approximately:
$\boxed{4.98}$

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QuestionFind the range and standard deviation of the set of data. $11,8,7,13,21 \square$
The range is $\square$ (Simplify your answer.)

Studdy Solution

STEP 1

1. The data set consists of the numbers: $11, 8, 7, 13, 21$ .
2. The range is the difference between the maximum and minimum values in the data set.
3. The standard deviation measures the amount of variation or dispersion in a set of values.

STEP 2

1. Calculate the range.
2. Calculate the standard deviation.

STEP 3

Identify the maximum and minimum values in the data set:
Maximum value = $21$
Minimum value = $7$

STEP 4

Calculate the range by subtracting the minimum value from the maximum value:
$\text{Range} = 21 - 7 = 14$

STEP 5

Calculate the mean (average) of the data set:
$\text{Mean} = \frac{11 + 8 + 7 + 13 + 21}{5} = \frac{60}{5} = 12$

STEP 6

Calculate the squared differences from the mean for each data point:
$(11 - 12)^2 = 1$
$(8 - 12)^2 = 16$
$(7 - 12)^2 = 25$
$(13 - 12)^2 = 1$
$(21 - 12)^2 = 81$

STEP 7

Calculate the variance by finding the average of the squared differences:
$\text{Variance} = \frac{1 + 16 + 25 + 1 + 81}{5} = \frac{124}{5} = 24.8$

STEP 8

Calculate the standard deviation by taking the square root of the variance:
$\text{Standard Deviation} = \sqrt{24.8} \approx 4.98$
The range is:
$\boxed{14}$
The standard deviation is approximately:
$\boxed{4.98}$

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QuestionFind the range and standard deviation of the set of data. 11,8,7,13,21□11,8,7,13,21 \square11,8,7,13,21□The range is □\square□ (Simplify your answer.)

Studdy Solution

STEP 1

1. The data set consists of the numbers: 11,8,7,13,21 11, 8, 7, 13, 21 11,8,7,13,21.2. The range is the difference between the maximum and minimum values in the data set.3. The standard deviation measures the amount of variation or dispersion in a set of values.

STEP 2

1. Calculate the range.2. Calculate the standard deviation.

STEP 3

Identify the maximum and minimum values in the data set:Maximum value = 21 21 21Minimum value = 7 7 7

STEP 4

Calculate the range by subtracting the minimum value from the maximum value:Range=21−7=14 \text{Range} = 21 - 7 = 14 Range=21−7=14

STEP 5

Calculate the mean (average) of the data set:Mean=11+8+7+13+215=605=12 \text{Mean} = \frac{11 + 8 + 7 + 13 + 21}{5} = \frac{60}{5} = 12 Mean=511+8+7+13+21​=560​=12

STEP 6

Calculate the squared differences from the mean for each data point:(11−12)2=1 (11 - 12)^2 = 1 (11−12)2=1(8−12)2=16 (8 - 12)^2 = 16 (8−12)2=16(7−12)2=25 (7 - 12)^2 = 25 (7−12)2=25(13−12)2=1 (13 - 12)^2 = 1 (13−12)2=1(21−12)2=81 (21 - 12)^2 = 81 (21−12)2=81

STEP 7

Calculate the variance by finding the average of the squared differences:Variance=1+16+25+1+815=1245=24.8 \text{Variance} = \frac{1 + 16 + 25 + 1 + 81}{5} = \frac{124}{5} = 24.8 Variance=51+16+25+1+81​=5124​=24.8

STEP 8

Calculate the standard deviation by taking the square root of the variance:Standard Deviation=24.8≈4.98 \text{Standard Deviation} = \sqrt{24.8} \approx 4.98 Standard Deviation=24.8​≈4.98 The range is:14 \boxed{14} 14​The standard deviation is approximately:4.98 \boxed{4.98} 4.98​

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QuestionFind the range and standard deviation of the set of data. $11,8,7,13,21 \square$
The range is $\square$ (Simplify your answer.)

1. The data set consists of the numbers: $11, 8, 7, 13, 21$ .
2. The range is the difference between the maximum and minimum values in the data set.
3. The standard deviation measures the amount of variation or dispersion in a set of values.

1. Calculate the range.
2. Calculate the standard deviation.

Identify the maximum and minimum values in the data set:
Maximum value = $21$
Minimum value = $7$

Calculate the range by subtracting the minimum value from the maximum value:
$\text{Range} = 21 - 7 = 14$

Calculate the mean (average) of the data set:
$\text{Mean} = \frac{11 + 8 + 7 + 13 + 21}{5} = \frac{60}{5} = 12$

Calculate the squared differences from the mean for each data point:
$(11 - 12)^2 = 1$
$(8 - 12)^2 = 16$
$(7 - 12)^2 = 25$
$(13 - 12)^2 = 1$
$(21 - 12)^2 = 81$

Calculate the variance by finding the average of the squared differences:
$\text{Variance} = \frac{1 + 16 + 25 + 1 + 81}{5} = \frac{124}{5} = 24.8$

Calculate the standard deviation by taking the square root of the variance:
$\text{Standard Deviation} = \sqrt{24.8} \approx 4.98$
The range is:
$\boxed{14}$
The standard deviation is approximately:
$\boxed{4.98}$