Practice Questions on Statistics - Advanced

Statistics is a branch of mathematics that involves the collection, organization, analysis, interpretation, and presentation of data. It helps us understand and interpret numerical information by transforming raw numbers into meaningful insights, and is used to make informed decisions in various fields. Statistics is the backbone of data-driven decision-making across industries and disciplines.

Important Formulas in Statistics

• Mean of a dataset :

• Variance (ungrouped data):Variance =

• Standard Deviation : SD =

• Mean of grouped data :

• Variance (grouped data) : Variance =

• Coefficient of Variation (CV): CV =

• Combined Mean for Two Groups:

• Combined Variance for Two Groups:

• Combined Standard Deviation:σc=σc2\sigma_c = \sqrt{\sigma_c^2}σc​=σc2​​

• Quartile Deviation (QD):QD =

• Mean Deviation about the Mean: MD =

• Variance for a Sample: Variance =

• Z-Score: Z =

• Interquartile Range (IQR):IQR = Q3−Q1

• Percentile Rank: P =

• Pearson correlation coefficient (r) : r =
  where,
  x_i,y_i = Individual data points in the datasets X and Y.
  = Mean of the X and Y dataset.

Read :

• Statistics In Math
• Basic Practice Questions on Statistics
• Statistics Solved Questions

Practice Questions on Statistics - Advanced

Question 1:Find the variance and standard deviation of the following dataset: 6, 8, 10, 12, 14
Solution:

Calculate the mean:

Mean

Compute squared deviations:

Variance == 16+4+0+4+16 / 5 ​=8

Standard Deviation =

Variance = 8, Standard Deviation = 2.83

Question 2:Find the variance and standard deviation for the following grouped data:

Solution:

Compute midpoints (x_i​): x_i=15, 25, 35, 45, 55

Compute mean

Compute and :

xi	fi
15	5	-21.43	459.26	2296.3
25	7	-11.43	130.67	914.69
35	8	-1.43	2.04	16.33
45	10	8.57	73.45	734.5
55	5	18.57	344.79	1723.95

• Variance:
  Variance =

• Standard Deviation:
  SD =

Question 3: The mean of a dataset is 50 and its standard deviation is 5. Calculate the coefficient of variation.
Solution:

Coefficient of Variation (CV) =

Question 4 :Find the combined standard deviation of two groups of students which have the following data:

• Group A:
• Group B:

Solution:

Combined mean:

Combined variance:

Combined standard deviation:

Question 5:Find the quartile deviation for the dataset: 5, 7, 8, 10, 12, 15, 18
Solution:

Arrange data in ascending order

Quartile Deviation:
QD= (Q₃−Q₁)/2 = (15−7)/2 = 4

Question 6:Find the mean deviation about the mean for the dataset: 3, 6, 9, 12, 15
Solution:

Mean:

Deviations:

Mean Deviation:

Question 7: Find the variance for the sample: 5, 7, 9, 11, 13
Solution:

Mean:

Variance:

Question 8: Find the Z-score for x = 80 if the dataset has a mean of 50 and a standard deviation of 15.
Solution:

Given,
x = 80
mean = 50
Standard deviation = 15

Z =

Question 9 :Find the range and interquartile range (IQR) for the following dataset:8, 12, 16, 20, 24, 28, 32, 36
Solution:

Range =

Quartiles:
Q1 =
Q3 =

IQR = Q₃ - Q₁ = 30 - 14 = 16

Question10: Find the percentile rank of x=18 in the dataset: 10, 12, 15, 18, 20, 25
Solution:

P =

Unsolved Practice Questions on Statistics

Question 1: A dataset contains the following values: 4, 7, 9, 10, 12, 14, 15, 18, 20, 25. Find the variance, standard deviation, and coefficient of variation.

Question 2: Calculate the Pearson correlation coefficient and interpret the result. the following paired data:

X = [1, 2, 3, 4, 5], Y = [2, 4, 6, 8, 10]

Question 3: Find the combined standard deviation for two groups of students with the following details:

• Group A: n₁ = 8,
• Group B: n₂ = 12,

Question 4:Calculate the quartile deviation for the following dataset: 5, 8, 12, 15, 18, 22, 25, 28, 30, 35.

Question 5:Find the mean deviation about the mean for the dataset: 10, 12, 14, 16, 18, 20, 22, 24.

Question 6: For the dataset 15, 18, 20, 24, 28, 30. calculate:

• Q1, Q3 and Interquartile Range (IQR).
• Range.

Question 7: In a sample of size 7 with values 6, 8, 10, 12, 14, 16, 18 calculate the Z-score for x = 16.

Question 8: For a grouped dataset with the following details, find the coefficient of variation:

Question 9: A dataset has a mean of 505050 and a standard deviation of 101010.

• Calculate the coefficient of variation.
• Find the Z-scores for x = 40 and x = 70.

Question 10 : For a dataset 3, 6, 9, 12, 15, 18, 21:

• Compute the variance.
• Compute the standard deviation.
• Calculate the mean deviation about the mean.

Answer key for Unsolved Questions

Answer 1:

• Mean:
• Variance: 38.84
• Standard Deviation: 6.23
• Coefficient of Variation: 46.46%

Answer 2: Correlation coefficient r = 1. Perfect positive linear relationship.

Answer 3:

• Combined Mean: 22.6
• Combined Variance: 41.4
• Combined Standard Deviation: 6.43

Answer 4:

• Q1 = 12.25, Q3=27.5
• Quartile Deviation: 7.63

Answer 5: Mean Deviation: 4

Answer 6:

• Q1=17Q1 = 17Q1=17, Q3=29Q3 = 29Q3=29, IQR = 121212
• Range: 151515

Answer 7: Z-score = 0.670.670.67

Answer 8:

• Mean: 12.512.512.5
• Standard Deviation: 6.326.326.32
• Coefficient of Variation: 50.56%50.56\%50.56%

Answer 9:

• Coefficient of Variation: 20%20\%20%
• Z-scores: −1-1−1 for x=40x = 40x=40, 222 for x=70x = 70x=70

Answer 10:

• Variance: 303030
• Standard Deviation: 5.485.485.48
• Mean Deviation: 4.84.84.8

Read More:

• Variance and Standard Deviation
• Coefficient of Variation