Basic Statistics Questions on Probability

Section-I
State whether the following statements are True or False.
1. Mean of the values 5, 4, 0, 3 is 3.
2. Half of the observations in a data set are greater than the median.
3. The total number of phone calls in a day, is the example of continuous data.
4. One or more outliers do not affect the value of the mean.
5. If mode= median= mean, then the distribution is not symmetric.
6. Let P(A)=0.15,P(B/A) = 0.4, if A and B are independent, then P(A and B)=0.60.

Section-II
(Multiple Choice Questions)

1. A researcher takes a sample of 120 employees of a company, the average age of company's employees is
a statistic.
a parameter.
the median.
a population.

2. The level of measurement of Student's grades, A,B, or C in a test is
Nominal
Ratio
Interval
Ordinal

3. The difference between the largest and the smallest data values is called
Variance
Class boundary
Range
None of the above answers is correct

4. A die with 6 faces is rolled. What is the probability that the number is greater than 4?
1/6
2/6
3/6
4/6

5. A distribution that has a long left tail is called:
Positive Skewed
Negative Skewed
Symmetric
both a and b

6. Find the original data from the stem and leaf plot

Stem Leaves
2 2 3
3 2 3 4
4 3 4 5
22,23,32,32,34,43,44,45
22,22,32,33,34,44,44,45
22,22,32,33,34,43,44,45
22,23,32,33,34,43,44,45

Section -III

Answer the following:

1.
a. Two coins are tossed, find the probability that one head only is obtained.
b. A card is drawn at random from a deck of cards. Find the probability of getting the King of hearts.
c. Two dice with 6 faces are rolled, find the probability that the sum is equal to 5.

2. Find the mean and standard deviation of the following sample data:

Marks(x) 1 3 5 7 9 11 13 15
Frequency(f) 3 3 4 14 7 4 3 4

3.
a. 29 machines were observed, and the number of defective parts was recorded for each machine. The resulting data is
1, 3, 2, 1, 1, 4, 2, 4, 1, 1, 1, 3, 1, 1, 1, 1, 2, 2, 1, 1, 4, 1, 1, 2, 1, 1, 1, 1, 3.
Construct a relative frequency distribution from the above data.

b. Construct a frequency histogram of the following frequency distribution

Class Interval Frequencies
50 - 60 13
60 - 70 27
70 - 80 43
80 - 90 31
90 - 100 9