Page 116 - WCS - Electrical

WORKSHOP CALCULATION & SCIENCE - CITS

7 The mean width of 12 iPads is 5.1 inches. The mean width of 8 Kindles is 4.8 inches. What is the total width
of the iPads and Kindles? What is the mean width of the 12 iPads and 8 Kindles?
Median
The median is a measure of central tendency in statistics. It is the middle value of a dataset when the values are
arranged in ascending or descending order. If the dataset has an odd number of observations, the median is the
middle value. If the dataset has an even number of observations, the median is the average of the two middle
values.
In other words, the median divides the dataset into two equal halves. It is less sensitive to extreme values or
outliers compared to the mean, making it a robust measure of central tendency, especially for skewed distributions.
The formula to find the median depends on whether the number of observations is odd or even. If the number
of observations (n) is odd, the median is the value at position (n+l)/2 in the ordered dataset. If the number of
observations (n) is even, the median is the average of the values at positions n/2 and (n/2)+1 in the ordered
dataset. The median is commonly used in various fields such as statistics, economics, and data analysis to
describe the central value of a dataset.
Example
1 Find the median of the following data

Data:4, 2, 7, 3, 10, 9, 13
Solution
Arrange the data in ascending order: 2, 3, 4, 7, 9, 10, 13. With 7 observations, the median is the 4th term, which
is 7.
2 Data:54,49,51,58,61,S2,54,60
Solution
Arrange the data in ascending order: 49, 51, 52, 54, 54, 58, 60, 61. With 8 observations, the median is the
average of the 4th and 5th terms, which is 54.
Mode
Mode is a statistical term that refers to the value that appears most frequently in a data set. It is one of the three
measures of central tendency, along with mean and median. The mode can be calculated by identifying the value
or values that occur most frequently in a data set. A data set can have one mode, more than one mode, or no
mode at all. The mode is particularly useful for categorical data, where it can reflect the most commonly found
characteristic, such as demographic information. It is also useful for ordinal variables, such as level of agreement
on a ranked scale. However, for quantitative data, such as reaction time or height, the mode may not be a helpful
measure of central tendency, as there are often many more possible values for quantitative data than there are
for categorical data, making it unlikely for values to repeat
Problem 1: Find the mode of the following dataset: 4, 8, 3, 2, 4, 7, 4, 8, 6, 4
Solution
The number 5 appears most frequently (four times), so the mode of the dataset is 5.
Problem 2: Find the mode of the following dataset: 11, 8, 16, 9, 11, 8, 16, 11, 9,16,8

Solution: To find the mode, we identify the number that occurs with the highest frequency. Here, the numbers 8,
11, and 16 all occur three times. Therefore, this dataset is trimodal, and the modes are 8, 11, and 16.
Relationship between mean, median and mode

(Mean - Median) = 1/3 (Mean - Mode) This formula quantifies the relationship between the mean, median, and
mode in a dataset. It highlights the differences between these measures and their positions within the distribution.
Understanding the relationship between mean, median, and mode is essential for interpreting the characteristics
of a dataset and gaining insights into its distribution and central tendency.
Problem 1: Dataset: 12, 15, 18, 20, 22, 25, 28, 30 Find the mean, mode, and median of the dataset and verify the
relationship between them.

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CITS : WCS - Electrical - Exercise 9