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Math  /  Data & Statistics

QuestionFind the range and standard deviation of the set of data. 8,11,8,11,11,13,158,11,8,11,11,13,15
The range is □\square (Simplify your answer.)

Studdy Solution

STEP 1

1. The set contains seven data points: 8,11,8,11,11,13,15 8, 11, 8, 11, 11, 13, 15 .
2. The range is the difference between the maximum and minimum values.
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 minimum and maximum values in the data set.
Minimum value: 8 8
Maximum value: 15 15

STEP 4

Calculate the range using the formula:
Range=Maximum value−Minimum value=15−8\text{Range} = \text{Maximum value} - \text{Minimum value} = 15 - 8
Range=7\text{Range} = 7

STEP 5

Calculate the mean of the data set.
Mean=8+11+8+11+11+13+157=777=11\text{Mean} = \frac{8 + 11 + 8 + 11 + 11 + 13 + 15}{7} = \frac{77}{7} = 11

STEP 6

Calculate the squared differences from the mean for each data point.
(8−11)2=9,(11−11)2=0,(8−11)2=9(8 - 11)^2 = 9, \quad (11 - 11)^2 = 0, \quad (8 - 11)^2 = 9 (11−11)2=0,(11−11)2=0,(13−11)2=4(11 - 11)^2 = 0, \quad (11 - 11)^2 = 0, \quad (13 - 11)^2 = 4 (15−11)2=16(15 - 11)^2 = 16

STEP 7

Calculate the variance by finding the average of the squared differences.
Variance=9+0+9+0+0+4+167=387≈5.43\text{Variance} = \frac{9 + 0 + 9 + 0 + 0 + 4 + 16}{7} = \frac{38}{7} \approx 5.43

STEP 8

Calculate the standard deviation by taking the square root of the variance.
Standard Deviation=5.43≈2.33\text{Standard Deviation} = \sqrt{5.43} \approx 2.33
The range is:
7 \boxed{7}
The standard deviation is approximately:
2.33 \boxed{2.33}

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