TMUA Data Analysis & Statistical Interpretation — Questions and Answers

Question 1: What is the mean of the numbers: 4, 8, 6, 10?

6
7 (Correct answer)
8
10

Correct answer: 7

The mean (or average) of a set of numbers is found by summing all the numbers and then dividing by the count of numbers. For 4, 8, 6, 10, the sum is 28. Dividing by 4 (the count), the mean is 28 / 4 = 7.

Question 2: Which value represents the median of the data set: 3, 5, 7, 9, 11?

5
7 (Correct answer)
9
11

Correct answer: 7

The median is the middle value in a data set when the numbers are arranged in order. In the ordered set 3, 5, 7, 9, 11, there are five numbers, and 7 is the exact middle value with two numbers before and two numbers after it.

Question 3: What is the mode of the following data: 2, 3, 3, 5, 7?

2
3 (Correct answer)
5
7

Correct answer: 3

The mode of a data set is the value that appears most frequently. In the given data set (2, 3, 3, 5, 7), the number 3 appears twice, which is more often than any other number. Therefore, 3 is the mode.

Question 4: Which graph type is best for showing parts of a whole?

Line graph
Histogram
Pie chart (Correct answer)
Bar graph

Correct answer: Pie chart

A pie chart is ideal for showing parts of a whole because it represents categories as slices of a circle, where each slice's size is proportional to its percentage of the total. This visual representation clearly illustrates how each component contributes to the overall sum.

Question 5: What does a high standard deviation indicate?

Values are close together
Data points vary greatly (Correct answer)
The data is skewed right
There are fewer outliers

Correct answer: Data points vary greatly

A high standard deviation indicates that the individual data points in a set are widely spread out from the mean. This means there is a large amount of variability or dispersion within the data. Conversely, a low standard deviation suggests data points are clustered closely around the mean.

Question 6: Which measure is affected most by outliers?

Mean (Correct answer)
Median
Mode
Range

Correct answer: Mean

The mean is calculated by summing all data points and dividing by the count, making it highly sensitive to extreme values (outliers). A single very large or very small outlier can significantly shift the mean. The median and mode are less affected as they rely on position or frequency rather than the exact value of every data point.

Question 7: Which statistic best represents the center of skewed data?

Mean
Mode
Median (Correct answer)
Variance

Correct answer: Median

For skewed data, the median is the best measure of central tendency because it is not significantly affected by extreme values or outliers. Unlike the mean, which gets pulled towards the tail of the skew, the median accurately represents the middle value of the data distribution. The mode only indicates the most frequent value, which may not be central.

Question 8: What is the range of the dataset: 4, 7, 10, 13?

7
8
9 (Correct answer)
10

Correct answer: 9

The range of a dataset is the difference between the highest and lowest values. In the dataset 4, 7, 10, 13, the maximum value is 13 and the minimum value is 4. Therefore, the range is 13 - 4 = 9.

Question 9: In a survey of 100 students, 60 said they liked math. What percentage is this?

40%
50%
60% (Correct answer)
70%

Correct answer: 60%

To calculate the percentage, you divide the part by the whole and multiply by 100. In this case, 60 students out of 100 liked math, so (60 / 100) * 100% equals 60%. This directly translates the fraction into a percentage.

TMUA Data Analysis & Statistical Interpretation

What is the mean of the numbers: 4, 8, 6, 10?