Descriptive Statistics and Probability Assignment
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TAKE AWAY ASSIGNMENT
MMA 104 - DESCRIPTIVE STATISTICS
SUBMISSION DATE 2/4/2026
1. Use a back to back stem and leaf to compare the exam marks for French and English in a class of 20 pupils.
French: 75, 69, 58, 58, 46, 44, 52, 50, 53, 78, 51, 61, 61, 45, 31, 44, 53, 66, 47, 57
English: 52, 58, 68, 77, 88, 85, 43, 44, 56, 65, 65, 79, 44, 71, 84, 72, 63, 69, 72, 79
2. The data below shows the heights of 30 athletes in a race calculate an estimate of the mean mode and median height.
Height (cm): $140 < x < 144$, $144 < x < 148$, $148 < x < 152$, $152 < x < 156$, $156 < x < 160$, $160 < x < 164$
No of students: 4, 5, 8, 7, 5, 1
3. Find the quartile deviation, the mean absolute deviation and the standard deviation of the data: 9, 3, 4, 2, 9, 5, 8, 4, 7, 4
4. The following measures were computed for a frequency distribution: Mean = 50, coefficient of Variation = 35% and Karl Pearson's Coefficient of Skewness SK = -0.25. Compute Standard Deviation, Mode and Median of the distribution.
5. The ranks of Volume and Density are given below. Calculate the Spearman rank difference correlation coefficient R.
Heights: 2 6 8 4 7 4 9.5 4 1 9.5
Weights: 9 1 9 4 5 9 2 7 6 3
6. Two tetrahedral (4-sided) symmetrical dice are rolled, one after the other. Find the probability that;
a) Both dice will land on the same number.
b) Each die will land on a number less than 3.
c) The two numbers will differ by at most 1.
7. As a foreign language, 40% of the students took Spanish and 30% took French, while 60% took at least one of these languages. What percent of students took both Spanish and French?
8. If a group consist of 8 men and 6 women, in how many ways can a committee of 5 be selected if:
a) The committee is to consist of 3 men and 3 women.
b) There are no restrictions on the number of men and women on the committee.
c) There must at least one man.
d) There must be at least one of each sex.
9. A die is loaded such that the probability of a face showing up is proportional to the face number. Determine the probability of each sample point.
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Step by Step Written Solution
In this lesson, we will solve question seven from the assignment, which focuses on set theory in probabilities. Let's look at the problem.
Probability and Set Theory
Question: Given 40% take Spanish, 30% take French, and 60% take at least one, find the percentage of students who take both.
Let's define our variables. We will let S represent the set of students who took Spanish and F represent the set of students who took French.
The problem states that 60 percent of students took at least one of these languages. In set notation, at least one is the union of sets S and F.
We are asked to find the percentage of students who took both Spanish and French. This refers to the intersection of the two sets.
To solve this, we use the Inclusion-Exclusion Principle for probability. This formula states that the probability of the union is equal to the sum of individual probabilities minus the probability of their intersection.
Using the Inclusion-Exclusion Principle
Now, let's rearrange the formula to isolate the intersection, which is the value we want to find.
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