Statistics Assignment: Heart Rate, Rice Weight, Probability

This statistics assignment delves into the analysis of heart rate data, rice weight distributions, and probability calculations. The assignment includes frequency distributions, graphical representations like histograms and frequency polygons, and calculations of central tendencies such as mean, median, and mode for both heart rate and rice weight data. It further explores probability concepts with conditional probability and ball-drawing scenarios. The solution presents step-by-step calculations and interpretations of statistical measures, including variance and standard deviation, to provide a comprehensive understanding of the data and its implications. The assignment is designed to reinforce statistical concepts through practical application and data analysis.

Running head: STATISTICS
Statistics
Name of the Student:
Name of the University:
Author’s note:

1STATISTICS
Table of Contents
Question 1..................................................................................................................................2
1.a)..........................................................................................................................................2
1. b)........................................................................................................................................2
1.c)..........................................................................................................................................2
Question 2..................................................................................................................................4
2.a)..........................................................................................................................................4
2.b).........................................................................................................................................5
Question 3..................................................................................................................................5
3.a)..........................................................................................................................................5
3.b).........................................................................................................................................6

2STATISTICS
Question 1.
1.a)
The data denotes the measurements (in beats per minute) of pulse rate obtained from a
random sample of 40 males and 40 females respectively. The data set is continuous in
nature.
1. b)
Table 1: Table of frequency distribution of heart beat of males
Table 2: Table of frequency distribution of heart beat of females
1.c)
Figure 1: Histogram plot of heart beat of males

3STATISTICS
50-59 60-69 70-79 80-89 90-99
0
2
4
6
8
10
12
14
16
18
Heart beat of Males
Age groups
Frequencies
Figure 2: Frequency polygon of heart beat of males
45 55 65 75 85 95 105
0
2
4
6
8
10
12
14
16
18
Heart beat of Males
Mid value of age groups
Frequencies
Figure 3: Histogram plot of heart beat of females

4STATISTICS
60-69 70-79 80-89 90-99 100-109
0
2
4
6
8
10
12
14
Heart beats of Females
Age groups
Frequency
Figure 4: Frequency polygon of heart beat of females
55 65 75 85 95 105 115
0
2
4
6
8
10
12
14
Heart beat of Females
Mid value of age groups
Frequency
Question 2.
2.a)

5STATISTICS
i) The mean weight of the 12 randomly selected bags of rice is 5.000833 kg (approx.).
ii) The mode weight of the bags of rice is 5 kg.
iii) The median weight of the bags of rice is 5 kg.
iv) The variance of the weight of bags of rice is 0.000227 kg (approx.).
v) The standard deviation of the weight of bags of rice is 0.01505 kg (approx.).
2.b)
The mean, median and median values of the distribution of rice are almost equal (≈ 5
kg). The equality of central tendencies such as mean, median and mode indicate the
symmetry of the distribution of weights of bags of rice.
The variance and standard deviation of weights of bags are insignificant. It indicates
that the central tendency is highly close to each other and scatterness of weights of bags is
very low.
Question 3.
3.a)
i) The probability that respondent answered yes, given that the respondent was a
female = The number of females who answerd yes
The number of females = 8
50 = 0.16.
ii) The probability that respondent was a male, given that the respondent answered
no = The number of males who answered no
The number of people who answered no = 18
60 = 0.3.

6STATISTICS
3.b)
An urn contains five red balls and four blue balls. The number of total balls is (5+4) = 9.
Two balls are drawn without replacement.
i) The probability that both balls are blue = (probability of being first ball blue *
probability of being second ball blue) =
Total number of blue balls
Total number of balls ∗Total number of blue balls−1
Total number of balls−1
= ( 4
9 *( 4−1)
( 9−1) ¿ = (
4
9∗3
8 ¿= 1
6
=0.166667
ii) The probability that first ball is a red ball = Totalnumber of red balls
Total number of balls = 5
9 =
0.555556