Statistics Measures of Variation Worksheet 1 PDF

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Name ______________________________________________________ Per ______ Statistics Measures of Variation Worksheet #1 (10 pts.) 1.) When finding population variance, you divide the sum of squares by ___________. A.) N

C.) N -1

B.) sum of x

D.) (sum of x) -1

2.) When finding sample variance, you divide the sum of squares by ___________. A.) n

C.) n -1

B.) sum of x

D.) (sum of x) -1

3.) Standard deviation is the ______________ of variance A.) Opposite

C.) Square

B.) Reciprocal

D.) Square root

4.) A set with no variation means all the elements are ____________. A.) A set distance from the mean

C.) Zero

B.) The same

D.) Nulls

𝟏

5.) Chebyshev’s Theorem states that at least 𝟏 − 𝒌𝟐 of the data must lie within k ______________ of the mean. A.) variations

C.) standard deviations

B.) deviations

D.) medians

6.) True or False: The method for finding the mean differs depending on if you are analyzing a population or a sample.

Finding Measures of Variation 7.) A= {𝟑, 𝟏𝟏, 𝟗, 𝟐, 𝟏} Find the following measure of A. A is a sample. [Some of these measures are review] 𝚺𝒙 = ____

Size= ___=____

Range = ____

mean=____=______

Median = ____

variance= ____=_______

standard deviation= ____=_______

CV = ____

Pearson’s Skew = ____

Skew direction:

Chebychev’s Theorem– Round to two decimal points when necessary. 8.) What percent of data must lie within 7 standard deviations of the mean? _______ 9.) If a data set has 𝑥 =8 and s= 1.5, what percent of the data must lie between 5 and 11? _______ 10.) A data set has n = 900, 𝑥 = 45 and s = 3. At least how many data points lie between 40 and 50? ____ 11.) In any data set, at least 80% of the data must lie within _________standard deviations of the mean. 12.) In a data set with n = 5,000, 𝑥 = 14, and s = 1.2, at least 4,200 data points must lie between _______ and _______, symmetric about the mean (S.A.M.) 13.) A data set has n = 300, 𝑥 = 12 and s = 1.5. At least how many data points lie between 9 and 15? ________

Estimating Measures of Variation 14.) Estimate the variance and standard deviation of the frequency table below by adding the columns 𝑥, 𝑓𝑥, 𝑑, 𝑑 2 and 𝑑 2 𝑓 . Data represents a sample. [First blanks are for the correct symbols.] Class [0 – 5) [5 – 10) [10 – 15) [15 – 20) [20 – 25) ∑

Frequency 8 10 3 2 1

Mean =___ ≈ ________ Weighted 𝑆𝑆𝑥 ≈ ________ Variance = ___ ≈ ________ Standard deviation = ___ ≈ _________

Measures of Variation Worksheet #1 Answer Key 1.) A 2.) C 3.) D 4.) B 5.) C 6.) False

7.) size: 𝑛 = 5 median: 3 CV = 86%

range: 10 variance: 𝑠 2 = 20.2 Pearson’s Skew: 1.47

8.) 97.96% 9.) 75% 10.) 576 11.) 2.24 12.) 11 and 17 13.) 225 14.) Mean (est.): 𝑥 = 7.9 Weighted Sum of Squares: 695.84 Variance (est.): 𝑠 2 = 30.254 Standard deviation (est.): 𝑠 = 5.5

𝚺𝒙 = 26

mean: 𝑥 = 5.2

standard deviation: 𝑠 = 4.49 Skew direction: Right...