100 Practice Questions with Step-by-Step Solutions
SECTION 1: DESCRIPTIVE STATISTICS
Questions 1–20 | Beginner to Intermediate
This section covers measures of central tendency, measures of dispersion, quartiles,
outliers, z-scores, and the interpretation of statistical data.
Question 1: Arithmetic Mean
Problem:
A student receives the following scores on five quizzes:
12, 15, 18, 20, 25
Calculate the arithmetic mean.
Solution:
The arithmetic mean is the sum of all observations divided by the number of observations.
Formula:
Mean = Sum of observations / Number of observations
Step 1: Add all the scores.
12 + 15 + 18 + 20 + 25 = 90
Step 2: Count the observations.
Number of observations = 5
Step 3: Divide the sum by the number of observations.
Mean = = 18
Final Answer: 18
,Interpretation: The student's average quiz score is 18.
Question 2: Median
Problem:
Find the median of the following dataset:
7, 12, 4, 15, 9, 10, 6
Solution:
The median is the middle value of an ordered dataset.
Step 1: Arrange the observations in ascending order.
4, 6, 7, 9, 10, 12, 15
Step 2: Count the observations.
There are 7 observations, an odd number.
Step 3: Find the middle position.
Middle position = (n + 1) / 2
= (7 + 1) / 2 = 4
Step 4: Identify the fourth observation.
The fourth observation is 9.
Final Answer: 9
Question 3: Mode
Problem:
A survey records the number of books read by six students in one month:
2, 3, 4, 3, 5, 3
Find the mode.
Solution:
,The mode is the value that occurs most frequently in a dataset.
Step 1: Count the frequency of each value.
● 2 occurs once.
● 3 occurs three times.
● 4 occurs once.
● 5 occurs once.
Step 2: Identify the most frequent value.
The value 3 occurs more frequently than any other value.
Final Answer: 3 books
Question 4: Range
Problem:
The weekly study hours of six students are:
8, 12, 15, 7, 20, 11
Calculate the range.
Solution:
The range is the difference between the largest and smallest observations.
Formula:
Range = Maximum value − Minimum value
Step 1: Identify the maximum value.
Maximum = 20
Step 2: Identify the minimum value.
Minimum = 7
Step 3: Subtract the minimum from the maximum.
Range = 20 − 7 = 13
Final Answer: 13 hours
Interpretation: The difference between the highest and lowest reported study times is 13
hours.
, Question 5: Finding a Missing Value from the Mean
Problem:
The mean of five numbers is 16. Four of the numbers are 12, 14, 18, and 20. Find the fifth
number.
Solution:
Formula:
Mean = Total sum / Number of observations
Step 1: Calculate the total sum of all five numbers.
Total sum = Mean × Number of observations
= 16 × 5 = 80
Step 2: Add the four known numbers.
12 + 14 + 18 + 20 = 64
Step 3: Subtract the known sum from the total sum.
Missing value = 80 − 64 = 16
Final Answer: 16
Question 6: Effect of an Extreme Value on the Mean
Problem:
The monthly earnings, in hundreds of dollars, of five students are:
8, 9, 10, 11, 12
A sixth observation of 50 is added. Calculate the new mean.
Solution:
Step 1: Calculate the sum of the original observations.
8 + 9 + 10 + 11 + 12 = 50
Step 2: Add the new observation.