Quantitative Methods Module 12: Summarizing and Arranging Data

This assignment solution focuses on summarizing and arranging data using quantitative methods. It covers measures of central tendency such as mean, median, and mode, along with measures of spread like range and quartiles. The solution demonstrates how to locate the median and quartiles for a large data set, and explains how to find the median when it falls between two data points. Furthermore, it includes arranging data using a stem and leaf plot, creating a grouped frequency table, and calculating the mean of a grouped frequency. The assignment also explores the five-number summary, box and whisker plots, and frequency polygons, providing examples of uniform, symmetrical, normal, and skewed distributions. Students can use this solution to understand key concepts and improve their data analysis skills, and find more resources on Desklib.

QUANTITATIVE METHODS
STUDENT ID:
[Pick the date]

1. Summarising data
a.) Mean, Median and Mode
b.) Mean
c.) The relevant formula for computation of median is given below.
d.) Median between the two data points is computed as shown below.
Median= ∑ of data points
2
e.) Mode is a statistical value that refers to a number which has the highest frequency in the
given data set.
f.) The difference between maximum value of data set and minimum value of data set is
termed as range.
Range = Maximum – Minimum
g.) Data points
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h.) 50% of data points would fall between lower and upper quartile.
i.) The relevant formula or equation for determination of the two quartiles is given below.
2. Arranging Data
i) First 5 data points
First 5 data points = 0.2, 0.4, 1.3, 1.7, 1.9
j.) Grouped frequency table
Class Interval Class Centre
(x)
Frequency
(f)
f*x Cumulative Frequency
0 ≤ x ≤ 5 2.5 2 5.0 2
5 ≤ x ≤ 10 7.5 3 22.5 5
k.) Mean of a grouped frequency
Mean=∑ f ∗x
∑ f = (5+22.5)
(2+3) = 27.5
5 =5.5
3. Summarising Data
l.) Measures of central tendency in 5 number summary = Median
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Measures of spread in 5 number summary = First and third quartile
m.) The 5 measures in box and whisker plot
n.) 25% of data points is represented by each whisker.
o.) Number of students got a test score of 70 or above
Frequency of class = 70-79 = 11
Frequency of class = 80- 89 = 6
Frequency of class = 89-99 = 3
Total number of students got a test score of 70 or above = 11 + 6 + 3 = 20
p.) Frequency polygon on histogram
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q.) Distribution and box plot
1.) A Uniform, Symmetrical Distribution
2.) A Normal, Symmetrical Distribution
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3.) A Negatively, Skewed Distribution
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4.) A Negatively, Skewed Distribution
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