Critical Thinking Questions: Measures of Central Tendency - Mean, Median and Mode

Statements Based Questions

Q1: Calculate the new mean if the number x is added to the data set with a current mean of m and n observations.
Statement 1: New mean = (mn + x) / n
Statement 2: New mean = (mn + x) / (n + 1)
Statement 3: New mean = m + x / n
(a) Only 1
(b) Only 2
(c) Only 3
(d) Only 1 and 3

Q2: The concept of median is illustrated. If the number (n) of observations arranged in ascending order, which of the following statements correctly describes how to find the median?
Statement 1: If n is odd, the median is the (n + 1)/2 th observation.
Statement 2: If n is even, the median is the average of the (n/2) th and (n/2 + 1) th observations.
Statement 3: The median is affected by extremely high or low values in the dataset, unlike the mean.
(a) Only 1
(b) Only 2
(c) Only 1 and 3
(d) All 1, 2, and 3

Q3: Consider the following set of numbers: {3, 5, 6, 9, 8, 5}. After arranging the data in ascending order and calculating the median and lower quartile (Q1), which of the following statements are true?
Statement 1: The median of the dataset is 5.5.
Statement 2: The lower quartile (Q1) is 5.
Statement 3: The upper quartile (Q3) is greater than the median.
(a) Only 1
(b) Only 2
(c) Only 1 and 3
(d) All 1, 2, and 3

Q4: A class of 60 students has their heights recorded. If the median height is 154.5 cm and the upper quartile is 155 cm, which of the following statements are true about the height distribution?
Statement 1: At least 50% of the students are 154.5 cm tall or shorter.
Statement 2: At least 25% of the students are taller than 155 cm.
Statement 3: The interquartile range of the students' heights is 2 cm.
(a) Only 1
(b) Only 2
(c) Only 1 and 3
(d) All 1, 2, and 3

Q5: Given the steps for estimating the mode from a histogram:
Statement 1: To estimate the mode, you need to draw straight lines from the corners of the modal class rectangle to the opposite corners of the highest rectangles on either side.
Statement 2: The point where the two lines intersect the x-axis gives the mode directly.
Statement 3: The mode can be estimated from a histogram regardless of whether the frequency distribution is continuous or discrete.
(a) Only 1
(b) Only 2
(c) Only 1 and 3
(d) Only 3

Q6: For constructing an ogive from the given frequency distribution, identify the correct statements:
Statement 1: An ogive is a graph that represents the cumulative frequency of each class interval.
Statement 2: The cumulative frequency is plotted against the upper-class limit of each interval on the x-axis.
Statement 3: The less than ogive will show a descending curve when plotted.
(a) Only 1
(b) Only 2
(c) Only 1 and 2
(d) Only 2 and 3

Q7: For a distribution of marks obtained by 200 students, if the lower quartile is represented by a point on the ogive graph with coordinates (42, 50), what does this indicate?
Statement 1: 50 students scored less than 42 marks.
Statement 2: 42 marks is the minimum score obtained by the top 75% of students.
Statement 3: The lower quartile corresponds to the score below which 25% of the students scored.
(a) Only 1
(b) Only 2
(c) Only 1 and 3
(d) All 1, 2, and 3

Q8: 35 marks, using the ogive, it was determined that 34 students scored below 35 marks. Consider the following statements:
Statement 1: 34 students failed the examination.
Statement 2: The point on the ogive representing 35 marks on the x-axis indicates the number of students who did not pass.
Statement 3: The percentage of students who did not pass the examination can be calculated as (34/200) × 100%.
(a) Only 1
(b) Only 2
(c) Only 1 and 3
(d) All 1, 2, and 3

Q9: Calculate the new mean if the number x is added to the data set with a current mean of m and n observations.
New mean = (mn + x) / (n + 1)
New mean = (mn + x) / n
New mean = m + x / n
(a) Only 1
(b) Only 2
(c) Only 3
(d) Only 1 and 3

Q10: Consider the following statements regarding the calculation of the mean:
Statement 1: For grouped data, the mean can be found by multiplying each midpoint of a class by the class frequency and dividing the sum of these products by the total number of observations.
Statement 2: When all observations in a data set are multiplied by a constant, the mean of the data set is also multiplied by that constant.
Statement 3: The arithmetic mean is not affected by extreme values in the data set.
(a) Only 1
(b) Only 1 and 2
(c) Only 2 and 3
(d) All 1, 2, and 3