Describing Data on a Single Variable
Which graph is best for displaying the frequency of categories?
Bar chart
Q: What type of plot displays data using quartiles and outliers?
Box plot
A histogram is used for which type of data?
Continuous data
Q: Which axis in a histogram usually represents the frequency?
Y-axis
Q: Which graph is most suitable for showing data trends over time?
Line graph
Q: Which measure of central tendency is most affected by extreme values?
Mean
The middle value of a sorted dataset is called ?
Median
If the mean = median = mode, the distribution is What?
Symmetrical
Q: Which measure of central tendency is appropriate for nominal data?
Mode
Q: The square of the standard deviation is called ?
Variance
Q: Which measure of dispersion uses all data points and has the same units as the data?
Standard deviatio
Q: Interquartile range (IQR) = ?
Q3 – Q1
Q: A standard deviation of zero means ?
All values are identical
Q: Which type of correlation shows both variables increasing together?
Positive correlation
Q: Name one graph that can display two categorical variables together.
Clustered bar chart
Q: The function that gives the probability of each value of a discrete random variable is called ?
A: Probability mass function (PMF)
Q: For any random variable, the total probability equals what?
A: 1
The graph of a probability density function (PDF) is always what?
Non-negative
If covariance = 0, it means what?
No linear relationship
If r = 0, it indicates what correlation.
A: No
A person records the daily rainfall in centimeters for a month. Is this a discrete or continuous random variable? Justify
Answer: Continuous random variable, because rainfall can be measured in fractional values.
A coin is tossed three times. Let X = number of heads obtained.
a) What type of random variable is X?
b) List all possible values of X.
a) Discrete random variable
b) {0, 1, 2, 3}
The lifetime (in hours) of an electric bulb is measured. What type of random variable is this and why?
Answer: Continuous random variable, because lifetime can take any real value within a range (not just integers).
A spinner has numbers 1, 2, 3, 4. Let Y = amount won in rupees if the spinner stops at a number. Is Y a discrete or continuous random variable? Explain.
Answer: Discrete, because it takes only a finite set of distinct values.
Identify the type of random variable:
X = height of students in a class
Z = number of red balls drawn from a bag in 4 trials
X → Continuous random variable
Z → Discrete random variable